EMO ClearBridge Energy Midstream Opportunity Fund Inc

Fund objective

The Fund’s investment objective is to provide long-term investors a high level of total return with an emphasis on cash distributions.

The Fund seeks to achieve its objective by investing primarily in energy midstream entities.

Letter from the chairman

Dear Shareholder,

We are pleased to provide the semi-annual report of ClearBridge Energy Midstream Opportunity Fund Inc. for the six-month reporting period ended May 31, 2021. Please read on for Fund performance information during the Fund’s reporting period.

As always, we remain committed to providing you with excellent service and a full spectrum of investment choices. We also remain committed to supplementing the support you receive from your financial advisor. One way we accomplish this is through our website, www.lmcef.com. Here you can gain immediate access to market and investment information, including:

We look forward to helping you meet your financial goals.

Sincerely,

Jane Trust, CFA

Chairman, President and Chief Executive Officer

June 30, 2021

Performance review

For the six months ended May 31, 2021, ClearBridge Energy Midstream Opportunity Fund Inc. returned 59.87% based on its net asset value (“NAV”)ⁱ and 80.38% based on its New York Stock Exchange (“NYSE”) market price per share. The Alerian MLP Indexⁱⁱ and the Lipper Energy MLP Closed-End Funds Category Averageⁱⁱⁱ returned 44.09% and 43.86%, respectively, over the same time frame. Please note that Lipper performance returns are based on each fund’s NAV.

During this six-month period, the Fund made distributions to shareholders totaling $0.71 per share. As of May 31, 2021, the Fund estimates that all of the distributions constituted a return of capital.* The performance table shows the Fund’s six-month total return based on its NAV and market price as of May 31, 2021. Past performance is no guarantee of future results.

All figures represent past performance and are not a guarantee of future results. Performance figures for periods shorter than one year represent cumulative figures and are not annualized.

** Total returns are based on changes in NAV or market price, respectively. Returns reflect the deduction of all Fund expenses, including management fees, operating expenses, and other Fund expenses. Returns do not reflect the deduction of brokerage commissions or taxes that investors may pay on distributions or the sale of shares.

† Total return assumes the reinvestment of all distributions, including returns of capital, if any, at NAV.

‡ Total return assumes the reinvestment of all distributions, including returns of capital, if any, in additional shares in accordance with the Fund’s Dividend Reinvestment Plan.

Looking for additional information?

The Fund is traded under the symbol “EMO” and its closing market price is available in most newspapers under the NYSE listings. The daily NAV is available online under the symbol “XEMOX” on most financial websites. Barron’s and The Wall Street Journal’s Monday edition both carry closed-end fund tables that provide additional information. In addition, the Fund issues a monthly press release that can be found on most major financial websites as well as www.lmcef.com (click on the name of the fund).

Performance review (cont’d)

In a continuing effort to provide information concerning the Fund, shareholders may call 1-888-777-0102 (toll free), Monday through Friday from 8:00 a.m. to 5:30 p.m. Eastern Time, for the Fund’s current NAV, market price and other information.

Thank you for your investment in ClearBridge Energy Midstream Opportunity Fund Inc. As always, we appreciate that you have chosen us to manage your assets and we remain focused on achieving the Fund’s investment goals.

Sincerely,

Jane Trust, CFA

Chairman, President and Chief Executive Officer

June 30, 2021

RISKS: The Fund is a non-diversified, closed-end management investment company designed primarily as a long-term investment and not as a trading vehicle. The Fund is not intended to be a complete investment program and, due to the uncertainty inherent in all investments, there can be no assurance that the Fund will achieve its investment objective. The Fund’s common stock is traded on the New York Stock Exchange. Similar to stocks, the Fund’s share price will fluctuate with market conditions and, at the time of sale, may be worth more or less than the original investment. Shares of closed-end funds often trade at a discount to their net asset value. Because the Fund is non-diversified, it may be more susceptible to economic, political or regulatory events than a diversified fund. The Fund’s investments are subject to a number of risks such as stock market risk, MLP and midstream entities risk, market events risk and portfolio management risk. MLP distributions are not guaranteed and there is no assurance that all distributions will be tax deferred. Investments in MLP securities and midstream entities are subject to unique risks. The Fund’s concentration of investments in energy-related MLPs and midstream entities subjects it to the risks of MLPs, midstream entities and the energy sector, including the risks of declines in energy or commodity prices, decreases in energy demand, adverse weather conditions, natural or other disasters, changes in government regulation, and changes in tax laws. Leverage may result in greater volatility of NAV and the market price of common shares, and increases a shareholder’s risk of loss. The Fund may make significant investments in derivative instruments. Derivative instruments can be illiquid, may disproportionately increase losses, and have a potentially large impact on Fund performance. The Fund may invest in small-capitalization or illiquid securities, which can increase the risk and volatility of the Fund. The Fund may also invest in money market funds, including funds affiliated with the Fund’s manager and subadviser.

All investments are subject to risk including the possible loss of principal. Past performance is no guarantee of future results. All index performance reflects no deduction for fees, expenses or taxes. Please note that an investor cannot invest directly in an index.

Fund at a glance^† (unaudited)

Investment breakdown (%) as a percent of total investments

Schedule of investments (unaudited)

May 31, 2021

See Notes to Financial Statements.

See Notes to Financial Statements.

Statement of operations (unaudited)

For the Six Months Ended May 31, 2021

See Notes to Financial Statements.

See Notes to Financial Statements.

Statement of cash flows (unaudited)

For the Six Months Ended May 31, 2021

See Notes to Financial Statements.

See Notes to Financial Statements.

See Notes to Financial Statements.

Financial highlights (cont’d)

See Notes to Financial Statements.

Notes to financial statements (unaudited)

1. Organization and significant accounting policies

ClearBridge Energy Midstream Opportunity Fund Inc. (the “Fund”) was incorporated in Maryland on April 5, 2011 and is registered as a non-diversified, closed-end management investment company under the Investment Company Act of 1940, as amended (the “1940 Act”). The Board of Directors authorized 100 million shares of $0.001 par value common stock. The Fund’s investment objective is to provide long-term investors a high level of total return with an emphasis on cash distributions. There can be no assurance that the Fund will achieve its investment objective.

The Fund seeks to achieve its objective by investing primarily in energy midstream entities. Under normal market conditions, the Fund invests at least 80% of its Managed Assets in energy midstream entities including entities structured as both partnerships and corporations (the 80% policy). For purposes of the 80% policy, the Fund considers investments in midstream entities as those entities that provide midstream services including the gathering, transporting, processing, fractionation, storing, refining, and distribution of oil, natural gas liquids and natural gas. The Fund considers an entity to be within the Energy sector if it derives at least 50% of its revenues from the business of exploring, developing, producing, gathering, transporting, processing, fractionating, storing, refining, distributing, mining or marketing natural gas, natural gas liquids (including propane), crude oil, refined petroleum products or coal. “Managed Assets” means net assets plus the amount of borrowings and assets attributable to any preferred stock of the Fund that may be outstanding.

The following are significant accounting policies consistently followed by the Fund and are in conformity with U.S. generally accepted accounting principles (“GAAP”). Estimates and assumptions are required to be made regarding assets, liabilities and changes in net assets resulting from operations when financial statements are prepared. Changes in the economic environment, financial markets and any other parameters used in determining these estimates could cause actual results to differ. Subsequent events have been evaluated through the date the financial statements were issued.

(a) Investment valuation. Equity securities for which market quotations are available are valued at the last reported sales price or official closing price on the primary market or exchange on which they trade. The valuations for fixed income securities (which may include, but are not limited to, corporate, government, municipal, mortgage-backed, collateralized mortgage obligations and asset-backed securities) and certain derivative instruments are typically the prices supplied by independent third party pricing services, which may use market prices or broker/dealer quotations or a variety of valuation techniques and methodologies. The independent third party pricing services typically use inputs that are observable such as issuer details, interest rates, yield curves, prepayment speeds, credit risks/spreads, default rates and quoted prices for similar securities. Investments in open-end funds are valued at the closing net asset value per share of each fund on the day of valuation. When the Fund holds securities or other assets that are

Notes to financial statements (unaudited) (cont’d)

denominated in a foreign currency, the Fund will normally use the currency exchange rates as of 4:00 p.m. (Eastern Time). If independent third party pricing services are unable to supply prices for a portfolio investment, or if the prices supplied are deemed by the manager to be unreliable, the market price may be determined by the manager using quotations from one or more broker/dealers or at the transaction price if the security has recently been purchased and no value has yet been obtained from a pricing service or pricing broker. When reliable prices are not readily available, such as when the value of a security has been significantly affected by events after the close of the exchange or market on which the security is principally traded, but before the Fund calculates its net asset value, the Fund values these securities as determined in accordance with procedures approved by the Fund’s Board of Directors.

The Board of Directors is responsible for the valuation process and has delegated the supervision of the daily valuation process to the Global Fund Valuation Committee (formerly known as Legg Mason North Atlantic Fund Valuation Committee prior to March 1, 2021) (the “Valuation Committee”). The Valuation Committee, pursuant to the policies adopted by the Board of Directors, is responsible for making fair value determinations, evaluating the effectiveness of the Fund’s pricing policies, and reporting to the Board of Directors. When determining the reliability of third party pricing information for investments owned by the Fund, the Valuation Committee, among other things, conducts due diligence reviews of pricing vendors, monitors the daily change in prices and reviews transactions among market participants.

The Valuation Committee will consider pricing methodologies it deems relevant and appropriate when making fair value determinations. Examples of possible methodologies include, but are not limited to, multiple of earnings; discount from market of a similar freely traded security; discounted cash-flow analysis; book value or a multiple thereof; risk premium/yield analysis; yield to maturity; and/or fundamental investment analysis. The Valuation Committee will also consider factors it deems relevant and appropriate in light of the facts and circumstances. Examples of possible factors include, but are not limited to, the type of security; the issuer’s financial statements; the purchase price of the security; the discount from market value of unrestricted securities of the same class at the time of purchase; analysts’ research and observations from financial institutions; information regarding any transactions or offers with respect to the security; the existence of merger proposals or tender offers affecting the security; the price and extent of public trading in similar securities of the issuer or comparable companies; and the existence of a shelf registration for restricted securities.

For each portfolio security that has been fair valued pursuant to the policies adopted by the Board of Directors, the fair value price is compared against the last available and next

available market quotations. The Valuation Committee reviews the results of such back testing monthly and fair valuation occurrences are reported to the Board of Directors quarterly.

The Fund uses valuation techniques to measure fair value that are consistent with the market approach and/or income approach, depending on the type of security and the particular circumstance. The market approach uses prices and other relevant information generated by market transactions involving identical or comparable securities. The income approach uses valuation techniques to discount estimated future cash flows to present value.

GAAP establishes a disclosure hierarchy that categorizes the inputs to valuation techniques used to value assets and liabilities at measurement date. These inputs are summarized in the three broad levels listed below:

The inputs or methodologies used to value securities are not necessarily an indication of the risk associated with investing in those securities.

The following is a summary of the inputs used in valuing the Fund’s assets carried at fair value:

(b) Net asset value. The Fund determines the net asset value of its common stock on each day the NYSE is open for business, as of the close of the customary trading session

Notes to financial statements (unaudited) (cont’d)

(normally 4:00 p.m. Eastern Time), or any earlier closing time that day. The Fund determines the net asset value per share of common stock by dividing the value of the Fund’s securities, cash and other assets (including interest accrued but not collected) less all its liabilities (including accrued expenses, borrowings, interest payables and the aggregate liquidation value (i.e., $100,000 per outstanding share) of the Mandatory Redeemable Preferred Stock (“MRPS”)), net of income taxes, by the total number of shares of common stock outstanding.

(c) Master limited partnerships. Entities commonly referred to as “MLPs” are generally organized under state law as limited partnerships or limited liability companies. The Fund intends to primarily invest in MLPs receiving partnership taxation treatment under the Internal Revenue Code of 1986, as amended (the “Code”), and whose interests or “units” are traded on securities exchanges like shares of corporate stock. To be treated as a partnership for U.S. federal income tax purposes, an MLP whose units are traded on a securities exchange must receive at least 90% of its income from qualifying sources such as interest, dividends, real estate rents, gain from the sale or disposition of real property, income and gain from mineral or natural resources activities, income and gain from the transportation or storage of certain fuels, and, in certain circumstances, income and gain from commodities or futures, forwards and options with respect to commodities. Mineral or natural resources activities include exploration, development, production, processing, mining, refining, marketing and transportation (including pipelines) of oil and gas, minerals, geothermal energy, fertilizer, timber or industrial source carbon dioxide. An MLP consists of a general partner and limited partners (or in the case of MLPs organized as limited liability companies, a managing member and members). The general partner or managing member typically controls the operations and management of the MLP and has an ownership stake in the partnership. The limited partners or members, through their ownership of limited partner or member interests, provide capital to the entity, are intended to have no role in the operation and management of the entity and receive cash distributions. The MLPs themselves generally do not pay U.S. federal income taxes. Thus, unlike investors in corporate securities, direct MLP investors are generally not subject to double taxation (i.e., corporate level tax and tax on corporate dividends). Currently, most MLPs operate in the energy and/or natural resources sector.

(d) Foreign investment risks. The Fund’s investments in foreign securities may involve risks not present in domestic investments. Since securities may be denominated in foreign currencies, may require settlement in foreign currencies or pay interest or dividends in foreign currencies, changes in the relationship of these foreign currencies to the U.S. dollar can significantly affect the value of the investments and earnings of the Fund. Foreign investments may also subject the Fund to foreign government exchange restrictions, expropriation, taxation or other political, social or economic developments, all of which affect the market and/or credit risk of the investments.

(e) Concentration risk. Concentration in the energy sector may present more risks than if the Fund were broadly diversified over numerous sectors of the economy. A downturn in the energy sector of the economy could have a larger impact on the Fund than on an investment company that does not concentrate in the sector. At times, the performance of securities of companies in the sector may lag the performance of other sectors or the broader market as a whole.

(f) Security transactions and investment income. Security transactions are accounted for on a trade date basis. Interest income (including interest income from payment-in-kind securities), adjusted for amortization of premium and accretion of discount, is recorded on the accrual basis. Dividend income is recorded on the ex-dividend date for dividends received in cash and/or securities. Foreign dividend income is recorded on the ex-dividend date or as soon as practicable after the Fund determines the existence of a dividend declaration after exercising reasonable due diligence. The cost of investments sold is determined by use of the specific identification method. To the extent any issuer defaults or a credit event occurs that impacts the issuer, the Fund may halt any additional interest income accruals and consider the realizability of interest accrued up to the date of default or credit event.

(g) Return of capital estimates. Distributions received from the Fund’s investments in MLPs generally are comprised of income and return of capital. The Fund records investment income and return of capital based on estimates made at the time such distributions are received. Such estimates are based on historical information available from each MLP and other industry sources. These estimates may subsequently be revised based on information received from the MLPs after their tax reporting periods are concluded.

For the six months ended May 31, 2021, the Fund estimated that approximately 87% of the MLP distributions received would be treated as a return of capital. The Fund recorded as return of capital the amount of $13,763,190 of dividends and distributions received from its investments.

Additionally, the Fund updated the return of capital estimates from the year ended November 30, 2020 based on actual amounts subsequently reported to the Fund. This resulted in an increase of $497,915 in dividends and distributions received from investments.

(h) Partnership accounting policy. The Fund records its pro rata share of the income (loss) and capital gains (losses), to the extent of distributions it has received, allocated from the underlying partnerships and accordingly adjusts the cost basis of the underlying partnerships for return of capital. These amounts are included in the Fund’s Statement of Operations.

(i) Distributions to shareholders. Distributions to common shareholders are declared and paid on a quarterly basis and are recorded on the ex-dividend date. The estimated

Notes to financial statements (unaudited) (cont’d)

characterization of the distributions paid to common shareholders will be either a dividend (ordinary income), distribution (return of capital) or combination of both. This estimate is based on the Fund’s operating results during the period. The Fund anticipates that 100% of its current period distribution will be comprised of return of capital. The actual tax characterization of the common stock distributions made during the current year will not be determined until after the end of the fiscal year when the Fund can determine it’s earnings and profits and, therefore, may differ from the preliminary estimates.

Distributions to holders of MRPS are accrued on a daily basis as described in Note 7 and are treated as an operating expense as required by GAAP. For tax purposes, the payments made to the holders of the Fund’s MRPS are treated as a dividend (ordinary income) or distribution (return of capital) similar to the treatment of distributions made to common shareholders as described above. The Fund anticipates that 100% of its current period distribution to the MRPS shareholders will be treated as return of capital. The actual tax characterization of the MRPS distributions made during the current year will not be determined until after the end of the fiscal year when the Fund can determine its earnings and profits and, therefore, may differ from the preliminary estimates.

(j) Compensating balance arrangements. The Fund has an arrangement with its custodian bank whereby a portion of the custodian’s fees is paid indirectly by credits earned on the Fund’s cash on deposit with the bank.

(k) Federal and other taxes. The Fund, as a corporation, is obligated to pay federal and state income tax on its taxable income. The Fund invests its assets primarily in MLPs, which generally are treated as partnerships for federal income tax purposes. As a limited partner in the MLPs, the Fund includes its allocable share of the MLP’s taxable income in computing its own taxable income. The Fund, and entities in which the Fund invests, may be subject to audit by the Internal Revenue Service or other applicable tax authorities. The Fund’s taxable income or tax liability for prior taxable years could be adjusted if there is an audit of the Fund, or of any entity that is treated as a partnership for tax purposes in which the Fund holds an equity interest. The Fund may be required to pay tax, as well as interest and penalties, in connection with such an adjustment.

Deferred income taxes reflect (i) taxes on unrealized gains (losses), which are attributable to the temporary difference between fair market value and book basis, (ii) the net tax effects of temporary differences between the carrying amounts of assets and liabilities for financial reporting purposes and the amounts used for income tax purposes and, as applicable, (iii) the net tax benefit of accumulated net operating losses, capital losses and tax credit carryforwards. To the extent the Fund has a deferred tax asset, consideration is given as to whether or not a valuation allowance is required. The need to establish a valuation allowance for deferred tax assets is assessed periodically by management of the Fund based on Financial Accounting Standards Board (“FASB”), Accounting Standards Codification Topic 740, Income Taxes (“ASC 740”) that it is more likely than not that some

portion or all of the deferred tax asset will not be realized. In the assessment for a valuation allowance, consideration is given to all positive and negative evidence related to the realization of the deferred tax asset. This assessment considers, among other matters, the nature, frequency and severity of current and cumulative losses, forecasts of future profitability (which are highly dependent on future allocations of taxable income and future cash distributions from the Fund’s MLP holdings), the duration of statutory carryforward periods and the associated risk that net operating losses, capital losses and tax credit carryforwards may expire unused.

For all open tax years and for all major jurisdictions, management of the Fund has concluded that there are no significant uncertain tax positions that would require recognition in the financial statements. Furthermore, management of the Fund is also not aware of any tax positions for which it is reasonably possible that the total amounts of unrecognized tax benefits will significantly change in the next twelve months.

The Fund may rely to some extent on information provided by the MLPs, which may not necessarily be timely, to estimate taxable income and gains allocable from the MLP units held in the portfolio and to estimate the associated deferred tax liability. Such estimates are made in good faith. From time to time, as new information becomes available, the Fund modifies its estimates or assumptions regarding the current and deferred tax liabilities.

The Fund’s policy is to classify interest and penalties associated with underpayment of federal and state income taxes, if any, as income tax expense on its Statement of Operations. The 2016 through 2020 tax years remain open and subject to examination by tax jurisdictions.

(l) Reclassification. GAAP requires that certain components of net assets be reclassified to reflect permanent differences between financial and tax reporting. These reclassifications have no effect on net assets or net asset value per share. During the six months ended May 31, 2021, the Fund had no reclassification.

2. Investment management agreement and other transactions with affiliates

Legg Mason Partners Fund Advisor, LLC (“LMPFA”) is the Fund’s investment manager and ClearBridge Investments, LLC (“ClearBridge”) is the Fund’s subadviser. LMPFA and ClearBridge are indirect, wholly-owned subsidiaries of Franklin Resources, Inc. (“Franklin Resources”).

Under the investment management agreement, the Fund pays LMPFA an annual fee, paid monthly, in an amount equal to 1.00% of the Fund’s average daily Managed Assets.

LMPFA provides administrative and certain oversight services to the Fund. LMPFA delegates to the subadviser the day-to-day portfolio management of the Fund. For its services, LMPFA pays ClearBridge a fee monthly, at an annual rate equal to 70% of the net management fee it receives from the Fund.

Notes to financial statements (unaudited) (cont’d)

During periods in which the Fund utilizes financial leverage, the fees paid to LMPFA will be higher than if the Fund did not utilize leverage because the fees are calculated as a percentage of the Fund’s assets, including those investments purchased with leverage.

Effective March 1, 2021, LMPFA implemented a voluntary investment management fee waiver of 0.05% that will continue until February 28, 2022.

During the six months ended May 31, 2021, fees waived and/or expenses reimbursed amounted to $57,699.

All officers and one Director of the Fund are employees of Franklin Resources or its affiliates and do not receive compensation from the Fund.

3. Investments

During the six months ended May 31, 2021, the aggregate cost of purchases and proceeds from sales of investments (excluding short-term investments) were as follows:

4. Derivative instruments and hedging activities

During the six months ended May 31, 2021, the Fund did not invest in derivative instruments.

5. Loan

The Fund has a revolving credit agreement with The Bank of Nova Scotia (“Credit Agreement”), which allows the Fund to borrow up to an aggregate amount of $75,000,000 and renews daily for a 179-day term, unless notice to the contrary is given to the Fund. Effective January 7, 2021, the Credit Agreement is subject to a scheduled commitment termination date of January 6, 2022, unless extended. The Fund pays a commitment fee on the unutilized portion of the loan commitment amount at an annual rate of 0.25%, except that the commitment fee is 0.15% in the event that the aggregate outstanding principal balance of the loan is equal to or greater than 75% of $75,000,000. The interest on the loan is calculated at a variable rate based on LIBOR plus any applicable margin. Securities held by the Fund are subject to a lien, granted to The Bank of Nova Scotia, to the extent of the borrowing outstanding and any additional expenses. The Fund’s Credit Agreement contains customary covenants that, among other things, may limit the Fund’s ability to pay distributions in certain circumstances, incur additional debt, change its fundamental investment policies and engage in certain transactions, including mergers and consolidations and require asset coverage ratios in addition to those required by the 1940 Act. In addition, the Credit Agreement may be subject to early termination under certain conditions and may contain other provisions that could limit the Fund’s ability to utilize borrowing under the agreement. At May 31, 2021, the Fund had $57,000,000 of borrowings outstanding per this credit agreement. Interest expense related to this loan for the six

months ended May 31, 2021 was $191,116. For the six months ended May 31, 2021, the Fund incurred commitment fees of $54,263. For the year ended May 31, 2021, based on the number of days during the reporting period that the Fund had a loan balance outstanding, the average daily loan balance was $32,065,934 and the weighted average interest rate was 1.20%.

6. Senior secured notes

At May 31, 2021, the Fund had $45,103,579 aggregate principal amount of fixed-rate senior secured notes (“Senior Notes”) outstanding. Interest expense related to the Senior Notes for the six months ended May 31, 2021 was $944,261. Costs incurred by the Fund in connection with the Senior Notes are recorded as a deferred charge and are amortized over the life of the notes. Securities held by the Fund are subject to a lien, granted to the Senior Notes holders, to the extent of the borrowings outstanding and any additional expenses. The Senior Notes holders and the lender have equal access to the lien (See Note 5).

On February 7, 2020, Series A Senior Notes in the amount of $27,420,382 matured. On October 15, 2020 Series F Senior Notes in the amount of $8,176,039 matured.

The table below summarizes the key terms of each series of Senior Notes at May 31, 2021.