UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 14A

(Rule 14a-101)

Proxy Statement Pursuant to Section 14(a) of the

Securities Exchange Act of 1934

(Amendment No.    )

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☐ Preliminary Proxy Statement

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☐ Definitive Proxy Statement

☒ Definitive Additional Materials

☐ Soliciting Material Pursuant to Section 240.14a-11(c) or Section 240.14a-12

CLEARBRIDGE ENERGY MIDSTREAM OPPORTUNITY FUND INC.

(Name of Registrant as Specified in Its Charter)

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CLEARBRIDGE ENERGY MIDSTREAM OPPORTUNITY FUND INC. (EMO) Please Vote on the WHITE Proxy Card. Your Vote Is Important. No Matter How Many or How Few Shares You Own March 7, 2023 Dear Stockholder: The ClearBridge Energy Midstream Opportunity Fund Inc. (the “Fund” or “EMO”) Board of Directors (the “Board”) is committed to creating sustainable, long-term superior performance for all stockholders. Your Board has a long track record of working with the Fund’s management team to drive strong returns and increase distributions for you. Ahead of our Annual Meeting of Stockholders on April 14, 2023 (the “Annual Meeting”), you have an important role to play in protecting the future of your investment in the Fund. Saba Capital Management, L.P. (“Saba Capital”), a hedge fund and dissident investor, is seeking to disrupt the oversight and management of the Fund. To protect the long-term value of your investment in the Fund, the Board unanimously recommends that you vote “FOR” the election of the Fund’s Board Nominee on the enclosed WHITE Proxy Card today. Your Board is committed to acting in the best interests of all stockholders. In contrast, Saba Capital is attempting to advance its own agenda to the detriment of the Fund’s long-term stockholders. Saba Capital has a long history of engaging in activist campaigns with closed-end funds in order to force a liquidity event that will enable the hedge fund to exit with a quick profit for itself to the potential detriment of long-term stockholders like you. You may receive materials from Saba Capital asking you to vote on a gold card or voting instruction form. We urge you NOT to return the gold proxy card, as that vote will not count as a vote in support of the Fund’s Board. If you vote your shares more than once, only your latest-dated proxy card counts. Your vote is important, no matter how many or how few shares you own. We urge you to support the Board that is taking continuous actions to generate and enhance value for you.

Your Board And Management Team Are Committed To Delivering Strong Financial Performance And Growing Distributions Under the Board’s leadership, the Fund has a strong track record of delivering competitive financial performance and growing distributions. Since the low economic points of the pandemic, when significant oil and gas market headwinds impacted the energy sector and those investing in it, the Board and Fund managers’ decisive actions have led to considerable growth in stockholder returns. As a result of these actions, the Fund delivered growth that significantly outpaced peer funds. HISTORY OF OUTPERFORMANCE: ANNUAL RETURNS BASED ON MARKET PRICE 2022 2021 74.80% 53.73% 40.16% 25.69% EMO Lipper Peer Average EMO Lipper Peer Average The Fund’s strong performance has allowed it to significantly increase its distributions to you, including growing distributions by 28.3% over the last five quarters.

The Fund’s solid performance has been driven by ClearBridge Investments, LLC’s (“ClearBridge”), the Fund’s sub-adviser, disciplined approach to investing in companies that meet three criteria: 1. Companies with free cash flow as they have a tendency to outperform the market and are well positioned to deliver accelerating distribution growth and share repurchases; 2. Companies poised to benefit from the recovery in U.S. oil production following the pandemic; and 3. Companies with growing exposure to exports of U.S. crude oil, natural gas and natural gas liquids. In 2022, ClearBridge continued to shift the Fund’s portfolio to improve performance through: Increased exposure to the Diversified Increased exposure to the Natural Decreased exposure to the Gathering Energy Infrastructure segment Gas Transportation & Storage & Processing segment (which (which meaningfully outperformed the segment (which meaningfully performed in line with the broader broader Midstream sector) outperformed the broader Midstream sector) Midstream sector) ClearBridge is confident that this investment approach positions the Fund well against the background of continued global economic headwinds that are impacting all funds across the industry. The Fund’s recent performance has been lauded by recognized industry experts: TOP TEN PERFORMER ONE OF “THE 10 BEST out of 447 traded closed-end funds CLOSED-END FUNDS (CEFS) identified on www.cefconnect.com, a TO BUY NOW” leading provider of closed-end fund by independent third-party personal information, in 2022 finance adviser Kiplinger in February 2023 Your Vote Is Important. Please Vote on the WHITE Proxy Card.

Taking Decisive Action To Address The Discount Between Share Price And NAV In addition to enhancing value and increasing distributions, the Board also proactively monitors the level of the discount of the Fund’s share price relative to its net asset value (NAV). In an effort to narrow the discount to NAV, your Board has worked with Fund management to: Repurchase more than $26 million since Increase the dividend each of the last five quarters the commencement of the repurchase program, resulting in an over $6 million Implement a fee waiver of 5 basis points (0.05%), increase to the Fund’s total net assets that lowering the Fund’s management fee well below its can be invested for the benefit of peer group average stockholders The Board is committed to advancing the Fund’s investment objective — delivering a high level of total return with an emphasis on cash distributions — over the long-term with the benefits of narrowing the discount to NAV in the short-term. Continued Success Of The Fund The Board is comprised of seven highly qualified members and is carefully constructed to ensure that we have the right mix of skills and diverse voices to achieve independent and well-rounded oversight of our strategy. SIX OF SEVEN BOARD MAJORITY ARE WOMEN ALL DIRECTORS BRING MEMBERS (including the Board Chair, Lead SKILLS, QUALIFICATIONS AND ARE INDEPENDENT Independent Director, Audit REQUISITE EXPERIENCE Committee Chair and Pricing and to oversee the Fund’s Valuation Committee Chair) operations and strategy As a common stockholder, you have the opportunity to protect the value of your investment by voting “FOR” the Fund’s nominee, Robert D. Agdern. Robert D. Agdern is an experienced business and legal professional with over 25 years of experience in the oil and gas industry and currently serves as the Fund’s Compliance Liaison. Mr. Agdern also held various leadership positions with Amoco Corporation, including Exploration and Production Company General Counsel and Executive Vice President — Natural Gas; Chemical Company General Counsel; and Associate General Counsel, Amoco Corporation. Mr. Agdern formerly served as Deputy General Counsel for BP PLC and as a Member of the Advisory Committee of the Dispute Resolution Research Center at the Kellogg Graduate School of Business, Northwestern University. Mr. Agdern has served on the Fund’s Board since 2015 and has extensive experience serving as a director for registered, closed-end investment companies.

Your Vote is Important, No Matter How Many or How Few Shares You Own You can vote by internet, telephone or by signing and dating the WHITE Proxy Card or Voting Instruction Form and mailing it in the envelope provided. If you have any questions about how to vote your shares or need additional assistance, please contact: Georgeson LLC: 1 (800) 868-1391 Forward Looking Statement Past performance is no guarantee of future results. The information provided is not intended to be a forecast of future events, a guarantee of future results or investment advice. All investments are subject to risk including the possible loss of principal. All benchmark performance reflects no deduction for fees, expenses or taxes. Please note that an investor cannot invest directly in a benchmark.

Saba Capital Is Following Its Standard Playbook to Squeeze Out A Short-Term Profit At YOUR EXPENSE Saba Capital is a dissident hedge fund that has a history of implementing initiatives intended to generate a short-term profit for itself that, in practice, can derail a fund’s ability to continue to enhance performance for its stockholders who invest in the fund for the long-term. By engaging in this proxy contest, we believe Saba Capital is advancing its own agenda of forcing a liquidity event that will enable them to exit with a quick profit while leaving a smaller, less flexible fund behind. In this case, Saba Capital disclosed that its nominee would, if elected, propose a liquidity event that could necessitate dramatic negative changes in the Fund’s investment approach and could create considerable negative tax implications, which may result in reduced distributions to common stockholders like you. PROTECT THE VALUE OF YOUR INVESTMENT Vote the Enclosed WHITE Proxy Card Today With the Board’s effective oversight, your Fund has a proven track record of delivering strong financial performance and stockholder returns. Whether or not you plan to attend the Annual Meeting, you have an opportunity to protect the value of your investment by voting on the WHITE Proxy Card “FOR” the Fund’s nominee.