Exhibit 5.1

Fulbright Tower • 1301 McKinney, Suite 5100 • Houston, Texas 77010-3095

Main: 713 651 5151 • Facsimile: 713 651 5246

October 4, 2012

Enbridge Energy Management, L.L.C.

1100 Louisiana Street, Suite 3300

Houston, Texas 77002

Ladies and Gentlemen:

We have acted as counsel to Enbridge Energy Management, L.L.C., a Delaware limited liability company (the “Company”), with respect to certain legal matters in connection with the registration under the Securities Act of 1933, as amended (the “Securities Act”), of the offer and sale by the Company from time to time, pursuant to Rule 415 under the Securities Act of common shares representing limited liability company interests in the Company (the “Listed Shares”).

We also have participated in the preparation of the Prospectus (the “Prospectus”) contained in the Registration Statement on Form S-3 (the “Registration Statement”) to which this opinion is an exhibit. The Securities will be offered in amounts, at prices and on terms to be determined in light of market conditions at the time of sale and to be set forth in supplements (each a “Prospectus Supplement”) to the Prospectus contained in the Registration Statement. Capitalized terms not defined herein shall have the meanings ascribed to them in the Prospectus.

In rendering the opinions set forth below, we have examined and relied upon (i) the Registration Statement, including the Prospectus, (ii) the Amended and Restated Limited Liability Company Agreement of the Company, as amended, and (iii) such certificates, statutes and other instruments and documents as we consider appropriate for purposes of the opinions hereafter expressed. As to various questions of fact material to this opinion, we have relied upon statements and certificates of officers and representatives of the Company. In addition, we reviewed such questions of law as we considered appropriate.

In connection with rendering the opinions set forth below, we have assumed that (i) all information contained in all documents reviewed by us is true and correct, (ii) all signatures on all documents examined by us are genuine, (iii) all documents submitted to us as originals are authentic, and all documents submitted to us as copies conform to the originals of those documents, (iv) the Registration Statement, and any amendments thereto (including post-effective amendments), will have become effective, (v) a Prospectus Supplement will have been prepared and filed with the Securities and Exchange Commission describing the Listed Shares offered thereby, (vi) all Listed Shares will be offered and sold in compliance with applicable federal and state securities laws and in the manner specified in the Registration Statement and the applicable Prospectus Supplement, and (vii) a definitive purchase, underwriting or similar agreement with respect to any of the Listed Shares offered will have been duly authorized and validly executed and delivered by the Company and the other parties thereto.

Based on the foregoing, and subject to the assumptions, qualifications, limitations, and exceptions set forth herein, we are of the opinion that:

AUSTIN • BEIJING • DALLAS • DENVER • DUBAI • HONG KONG • HOUSTON • LONDON • LOS ANGELES • MINNEAPOLIS

MUNICH • NEW YORK • PITTSBURGH-SOUTHPOINTE • RIYADH • SAN ANTONIO • ST. LOUIS • WASHINGTON DC

www.fulbright.com

When (i) the Company has taken all necessary action to approve the issuance of the Listed Shares, the terms of the offering and related matters and (ii) the Listed Shares have been issued and delivered in accordance with the terms of the applicable definitive purchase, underwriting or similar agreement approved by the Company upon payment of the consideration therefor provided for therein, then the Listed Shares will be validly issued, fully paid and nonassessable.

The opinions expressed herein are limited exclusively to the General Corporation Law of the State of Delaware, the Delaware Revised Uniform Limited Partnership Act, the Delaware Limited Liability Company Act and the applicable provisions of the Delaware constitution and reported decisions concerning such laws, the laws of the State of Texas, the laws of the State of New York and the federal laws of the United States of America, and we are expressing no opinion as to the effect of the laws of any other jurisdiction.

We hereby consent to the references to this firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to the Registration Statement. By giving such consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Very truly yours,

/s/ Fulbright & Jaworski L.L.P.