Exhibit 3.4

CERTIFICATE OF AMENDMENT

TO THE

FIFTH AMENDED AND RESTATED

CERTIFICATE OF INCORPORATION

OF

ENTEROMEDICS INC.

I, Greg S. Lea, certify that:

1. The following resolution was duly adopted and approved by the board of directors of EnteroMedics Inc. (the “Corporation”) at a meeting of the board of directors held on February 15, 2012, in accordance with the applicable provisions of Section 242 of the General Corporation Law of the State of Delaware:

RESOLVED, that Article IV, Section 1 of the Fifth Amended and Restated Certificate of Incorporation of EnteroMedics Inc. is hereby amended and restated to read in full as follows:

“1. Authorized Stock. The Corporation is authorized to issue two classes of shares to be designated respectively Preferred Stock, par value $0.01 per share, and Common Stock, par value $0.01 per share. The total number of shares of Preferred Stock authorized is 5,000,000. The total number of shares of Common Stock authorized is 125,000,000.”

2. The foregoing amendment was duly adopted by the stockholders of the Corporation in accordance with Section 242 of the General Corporation Law of the State of Delaware on May 9, 2012 at an Annual Meeting of the Stockholders of the Corporation, and such resolution has not been subsequently modified or rescinded.

Dated: May 9, 2012