EX-5.1

Exhibit 5.1

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Capital Clean Energy Carriers Corp.

3, Iassonos Street

Piraeus, Athens

18537, Greece

January 27, 2025

Prospectus Supplement – Exhibit 5.1 Opinion

Dear Sirs:

We have acted as special counsel as to matters of the law of the Republic of the Marshall Islands (“Marshall Islands Law”) for Capital Clean Energy Carriers Corp., a Marshall Islands corporation (the “Company”), in connection with the registration of the issuance and sale from time to time by the Company of common shares, par value $0.01 per share, having an aggregate gross sales price of up to $75,000,000 (the “Shares”) pursuant to an Open Market Sales Agreement^SM, dated January 27, 2025 (the “Sales Agreement”), between the Company and Jefferies LLC.

As such counsel, we have examined originals or copies (certified or otherwise identified to our satisfaction) of the following documents:

(i)

the registration statement on Form F-3 (File No. 333-282610) (the “Registration Statement”) which became effective with the Securities and Exchange Commission on October 24, 2024 and the prospectus included therein (the “Base Prospectus”), and the prospectus supplement filed on the date hereof (the “Prospectus Supplement”);

(ii)

the Sales Agreement; and

(iii)

such corporate records, certificates, agreements, documents or other instruments, and such certificates or comparable documents of public officials and of officers and representatives of the Company as we have deemed relevant and necessary.

In such examination, we have assumed: (a) the legal capacity of each natural person, (b) the genuineness of all signatures (including electronic signatures) and the authenticity of all documents submitted to us as originals, (c) the conformity to original documents of all documents submitted to us as conformed or

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photostatic copies, (d) that the documents reviewed by us in connection with the rendering of the opinion set forth herein are true, correct, and complete, and (e) the truthfulness of each statement as to all factual matters contained in any document or certificate encompassed within the due diligence review undertaken by us.

In rendering this opinion, we have also assumed:

(i)

that the issuance and sale of the Shares complies in all respects with the terms, conditions and restrictions set forth in the Registration Statement, Base Prospectus, the Prospectus Supplement, the Sales Agreement and all of the instruments and other documents relating thereto or executed in connection therewith, and will comply with the Securities Act;

(ii)

that the Sales Agreement has been duly and validly authorized, executed and delivered by the parties thereto (other than the Company);

(iii)

the validity and enforceability of the Sales Agreement against the parties thereto; and

(iv)

(a) the dollar amount of common shares registered under the effective Registration Statement (b) the number or dollar amount of common shares of the Company permitted to be sold under Form F-3 (including General Instruction I.B.5 thereof, if applicable), and (c) the dollar amount of common shares for which the Company has filed a prospectus relating to the Shares in each case equals or exceeds $75 million.

As to any questions of fact material to our opinion, we have, when relevant facts were not independently established, relied upon the aforesaid certificates or comparable documents, and the representations and warranties of the Company contained in the Sales Agreement. We have not independently verified the facts so relied on.

We have assumed that (i) the Company will have sufficient authorized but unissued common shares on the date of any issuance of Common Shares, less common shares issuable upon exercise, conversion or exchange of any outstanding securities of the Company or otherwise reserved from the Company’s authorized capital stock and (ii) that the aggregate gross sales price of all Shares sold by the Company pursuant to the Sales Agreement (at the respective relevant times of sale) under the Sales Agreement will remain at or below $75,000,000, and that that each Share will not be issued below $1.00 per Share (as adjusted for any reverse stock splits) and never below the par value thereof, nor will be issued in fractional shares, and will be issued on or before October 24, 2027.

This opinion letter is limited to Marshall Islands Law. We expressly disclaim any responsibility to advise of any development or circumstance of any kind, including any change of law or fact that may occur after the date of this opinion letter that might affect the opinion expressed herein.

Based on the foregoing, and having regard to legal considerations which we deem relevant, and subject to the qualifications, limitations and assumptions set forth herein, we are of the opinion that when the Shares are issued and delivered against receipt of full payment therefor by the Company in accordance with the terms of the Sales Agreement, the Registration Statement, and the Prospectus Supplement, the Shares will be validly issued, fully paid and nonassessable.

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We consent to the filing of this opinion as an exhibit to the Registration Statement and Prospectus Supplement and to the discussion of this opinion in the Registration Statement and Prospectus Supplement, and to the references to our firm in the Registration Statement, Base Prospectus and the Prospectus Supplement. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act, nor do we admit that we are experts with respect to any part of the Registration Statement within the meaning of the term “expert” as used in the Securities Act.

Very truly yours,

Watson Farley & Williams LLP

/s/ Watson Farley & Williams LLP