<PAGE>   1
                                                                     EXHIBIT 3.1
                            CERTIFICATE OF AMENDMENT
                                     TO THE
                AMENDED AND RESTATED CERTIFICATE OF INCORPORATION
                                       OF
                              NET PERCEPTIONS, INC.

                        -------------------------------


                     Pursuant to Section 242 of the General
                    Corporation Law of the State of Delaware

                        -------------------------------

                  Net Perceptions, Inc., a Delaware corporation (hereinafter
called the "Corporation"), does hereby certify as follows:

                  FIRST: The first paragraph of Article IV of the Corporation's
Amended and Restated Certificate of Incorporation is hereby amended to read in
its entirety as set forth below:

                  The Corporation is authorized to issue two classes of stock to
                  be designated common stock ("Common Stock") and preferred
                  stock ("Preferred Stock"). The number of shares of Common
                  Stock authorized to be issued is One Hundred Million
                  (100,000,000), par value $.0001 per share, and the number of
                  shares of Preferred Stock authorized to be issued is Ten
                  Million (10,000,000), par value $.0001 per share.

                  SECOND: The foregoing amendment was duly adopted in accordance
with Section 242 of the General Corporation Law of the State of Delaware.

                  IN WITNESS WHEREOF, Net Perceptions, Inc. has caused this
Certificate to be duly executed in its corporate name this 25th day of May,
2000.
                                  Net Perceptions, Inc.
                                  By:/s/ Thomas M. Donnelly
                                     -----------------------------------------
                                  Name:  Thomas M. Donnelly
                                  Title: Senior Vice President, Chief Financial
                                  Officer and Secretary

<PAGE>   2
                                                                     EXHIBIT 3.1



                              AMENDED AND RESTATED
                         CERTIFICATE OF INCORPORATION OF
                              NET PERCEPTIONS, INC.
                             A DELAWARE CORPORATION

                     (PURSUANT TO SECTIONS 228, 242 AND 245
                    OF THE DELAWARE GENERAL CORPORATION LAW)


                  Net Perceptions, Inc., a corporation organized and existing
under the General Corporation Law of the State of Delaware (the "General
Corporation Law")

                  DOES HEREBY CERTIFY:

                  FIRST: That this corporation was originally incorporated on
July 3, 1996, pursuant to the General Corporation Law.

                  SECOND: That the Board of Directors duly adopted resolutions
proposing to amend and restate the Amended and Restated Certificate of
Incorporation of this corporation, declaring said amendment and restatement to
be advisable and in the best interests of this corporation and its stockholders,
and authorizing the appropriate officers of this corporation to solicit the
consent of the stockholders therefor, which resolution setting forth the
proposed amendment and restatement is as follows:

                  "RESOLVED, that the Amended and Restated Certificate of
Incorporation of this corporation, as amended, be amended and restated in its
entirety as follows:

                                    ARTICLE I

                  The name of the corporation is Net Perceptions, Inc. (the
"Corporation").

                                   ARTICLE II

                  The address of the registered office of this corporation in
the State of Delaware is 15 E. North Street, in the City of Dover, County of
Kent. The name of its registered agent at such address is Incorporating
Services, Ltd.





<PAGE>   3
                                                                     EXHIBIT 3.1

                                   ARTICLE III

                  The nature of the business or purposes to be conducted or
promoted is to engage in any lawful act or activity for which corporations may
be organized under the General Corporation Law of Delaware.

                                   ARTICLE IV

                  The Corporation is authorized to issue two classes of stock to
be designated common stock ("Common Stock") and preferred stock ("Preferred
Stock"). The number of shares of Common Stock authorized to be issued is Fifty
Million (50,000,000), par value $.0001 per share, and the number of shares of
Preferred Stock authorized to be issued is Five Million (5,000,000) par value
$.0001 per share.

                  The Preferred Stock may be issued from time to time in one or
more series, without further stockholder approval. The Board of Directors is
hereby authorized, in the resolution or resolutions adopted by the Board of
Directors providing for the issue of any wholly unissued series of Preferred
Stock, within the limitations and restrictions stated in this Amended and
Restated Certificate, to fix or alter the dividend rights, dividend rate,
conversion rights, voting rights, rights and terms of redemption (including
sinking fund provisions), the redemption price or prices, and the liquidation
preferences of any wholly unissued series of Preferred Stock, and the number of
shares constituting any such series and the designation thereof, or any of them,
and to increase or decrease the number of shares of any series subsequent to the
issue of shares of that series, but not below the number of shares of such
series then outstanding. In case the number of shares of any series shall be so
decreased, the shares constituting such decrease shall resume the status that
they had prior to the adoption of the resolution originally fixing the number of
shares of such series.

                                    ARTICLE V

                  Except as otherwise provided in this Amended and Restated
Certificate, in furtherance and not in limitation of the powers conferred by
statute, the Board of Directors is expressly authorized to make, repeal, alter,
amend and rescind any or all of the Bylaws of the Corporation.






<PAGE>   4
                                                                     EXHIBIT 3.1

                                   ARTICLE VI

                  The number of directors of the Corporation shall be fixed from
time to time by a bylaw or amendment thereof duly adopted by the Board of
Directors.

                                   ARTICLE VII

                  Elections of directors need not be by written ballot unless
the Bylaws of the Corporation shall so provide.

                                  ARTICLE VIII

                  Except as otherwise provided in this Amended and Restated
Certificate of Incorporation, any action required or permitted to be taken by
the stockholders of the Corporation must be effected at an annual or special
meeting of the stockholders of the Corporation, and may not be effected by any
consent in writing of such stockholders.

                                   ARTICLE IX

                  A director of the Corporation shall not be personally liable
to the Corporation or its stockholders for monetary damages for breach of
fiduciary duty as a director, except for liability (i) for any breach of the
director's duty of loyalty to the Corporation or its stockholders, (ii) for acts
or omissions not in good faith or which involve intentional misconduct or a
knowing violation of law, (iii) under Section 174 of the Delaware General
Corporation Law, or (iv) for any transaction from which the director derived any
improper personal benefit. If the Delaware General Corporation Law is amended
after approval by the stockholders of this Article to authorize corporate action
further eliminating or limiting the personal liability of directors then the
liability of a director of the Corporation shall be eliminated or limited to the
fullest extent permitted by the Delaware General Corporation Law as so amended.

                  Any repeal or modification of the foregoing provisions of this
Article IX by the stockholders of the Corporation shall not adversely affect any
right or protection of a director of the Corporation existing at the time of, or
increase the liability of any director of this Corporation with respect to any
acts or omissions of such director occurring prior to, such repeal or
modification.






<PAGE>   5
                                                                     EXHIBIT 3.1

                                    ARTICLE X


                  In addition to any vote of the holders of any class or series
of the stock of this Corporation required by law or by this Amended and Restated
Certificate of Incorporation, the affirmative vote of the holders of a majority
of the voting power of all of the then outstanding shares of capital stock of
the Corporation entitled to vote generally in the election of directors, voting
together as a single class, shall be required to amend or repeal the provisions
of Article I, Article II, and Article III of this Amended and Restated
Certificate of Incorporation. Notwithstanding any other provision of this
Amended and Restated Certificate of Incorporation or any provision of law which
might otherwise permit a lesser vote or no vote, but in addition to any vote of
the holders of any class or series of the stock of this Corporation required by
law or by this Amended and Restated Certificate of Incorporation, the
affirmative vote of the holders of at least seventy-five percent (75%) of the
voting power of all of the then outstanding shares of the capital stock of the
Corporation entitled to vote generally in the election of directors, voting
together as a single class, shall be required to amend or repeal any provision
of this Amended and Restated Certificate of Incorporation not specified in the
preceding sentence.

                                     * * * *
                  THIRD: The foregoing Amended and Restated Certificate of
Incorporation has been duly adopted by the Corporation's Board of Directors in
accordance with the applicable provisions of Section 245 of the General
Corporation Law of the State of Delaware.

                  IN WITNESS WHEREOF, the undersigned has signed this
Certificate this 28th day of April, 1999.


                                       /s/ Steven J. Snyder
                                       -----------------------------------------
                                       Steven J. Snyder
                                       President and Chief Executive Officer

ATTEST:


/s/ Thomas M. Donnelly
----------------------
Thomas M. Donnelly
Secretary