<PAGE>
                                                                    EXHIBIT 3(h)

                            CERTIFICATE OF AMENDMENT

              OF AMENDED AND RESTATED CERTIFICATE OF INCORPORATION

                                      *****

     Regent Communications, Inc., a corporation organized and existing under and
by virtue of the General Corporation Law of the State of Delaware, DOES HEREBY
CERTIFY:

     FIRST: That at a meeting of the Board of Directors of Regent
Communications, Inc., resolutions were duly adopted setting forth a proposed
amendment to the Amended and Restated Certificate of Incorporation of such
corporation, declaring such amendment to be advisable and directing that the
proposed amendment be submitted to stockholders for their approval at the
following annual meeting. The resolution setting forth the proposed amendment is
as follows:

               "RESOLVED, subsection A, Article FOURTH of the Amended and
               Restated Certificate of Incorporation of Regent Communications,
               Inc. be hereby amended as follows:

               "A. Authorized Capital Stock. The total number of shares of all
               classes of Stock which the Corporation shall have authority to
               issue is One Hundred Forty Million (140,000,000) shares,
               consisting of a class of One Hundred Million (100,000,000) shares
               of Common Stock, par value of $.01 per share, and a class of
               Forty Million (40,000,000) shares of Preferred Stock, par value
               of $.01 per share."

               FURTHER RESOLVED, that the Board of Directors is fully authorized
               and empowered to implement the increase in authorized shares
               pursuant to the foregoing resolution without further action by
               the stockholders at such time as the Board of Directors shall
               deem appropriate and, to the extent allowable by law, either all
               at one time or partially in two or more stages as the Board of
               Directors shall deem advisable and in the best interests of the
               Corporation, and that any Certificate of Amendment to the Amended
               and Restated Certificate of Incorporation by which the aggregate
               number of authorized shares is increased pursuant to these
               resolutions shall be deemed to be approved by the same
               affirmative vote of the voting power of the Company as approved
               these resolutions."

<PAGE>

     SECOND: That, thereafter, on May 18, 2000, pursuant to a resolution of its
Board of Directors, an annual meeting of the stockholders of Regent
Communications, Inc. was duly called and held, upon notice in accordance with
Section 222 of the General Corporation Law of the State of Delaware, at which
meeting the necessary number of shares as required by statute were voted in
favor of the amendment.

     THIRD: That the amendment was duly adopted in accordance with the
provisions of Section 242 of the General Corporation Law of the State of
Delaware.

     IN WITNESS WHEREOF, Regent Communications, Inc. has caused this certificate
to be signed by Terry S. Jacobs, its Chairman and Chief Executive Officer, this
thirteenth day of March, 2002.

                                               REGENT COMMUNICATIONS, INC.

                                               By: /s/ TERRY S. JACOBS
                                                   -----------------------------
                                                   Terry S. Jacobs, Chairman and
                                                   Chief Executive Officer