<PAGE>
 
                                                                    Exhibit 3.01
                                                                    ------------
                     

                               DAVOX CORPORATION

                            CERTIFICATE OF AMENDMENT

                                       OF

                     RESTATED CERTIFICATE OF INCORPORATION

     Davox Corporation, a corporation organized and existing under and by virtue
of the General Corporation Law of the State of Delaware does hereby certify:

     FIRST:  That the Board of Directors of said corporation, at a regularly
scheduled meeting at which all of the members of the Board of Directors were
present and acting throughout, duly adopted a resolution proposing and declaring
advisable the following amendment to the Restated Certificate of Incorporation
of said corporation:

     RESOLVED, to recommend to the Stockholders of the Corporation, as
advisable, approval of the proposal to amend the Restated Certificate of
Incorporation of the Corporation by deleting the first sentence of Article
FOURTH thereof, and substituting therefor the following:

          The total number of shares of stock which the corporation shall have
          the authority to issue is Ten Million (10,000,000) shares of Common
          Stock, and the par value of each such share is Ten Cents ($.10),
          amounting in the aggregate to One Million Dollars ($1,000,000).

     SECOND:  That thereafter, the stockholders of said Corporation, by vote of
3,633,812 shares of Common Stock, constituting the necessary number of shares as
required by statute, voted in favor of the amendment.

     THIRD:  That the amendment herein set forth has been duly adopted in
accordance with the provisions of Section 242 of the General Corporation Law of
the State of Delaware.
<PAGE>
 
     IN WITNESS WHEREOF, Davox Corporation has caused its corporate seal to be
hereunto affixed and this certificate to be signed by its President and its
Assistant Secretary this 31st day of July 1990.

                                    DAVOX CORPORATION
 

                                    By: /s/ Daniel A. Hosage
                                        --------------------------
                                        Daniel A. Hosage
                                        President


ATTEST:


/s/  Timothy C. Maguire
-------------------------------
Timothy C. Maguire
Assistant Secretary
<PAGE>
 
                                    RESTATED

                          CERTIFICATE OF INCORPORATION

                                       OF

                               DAVOX CORPORATION


     Davox Corporation, a corporation organized and existing under the General
Corporation Law of the State of Delaware, DOES HEREBY CERTIFY:

     1.   That the original Certificate of Incorporation of said corporation was
filed with the Secretary of State of the State of Delaware of June 15, 1982, and
that the name under which the corporation was originally incorporated was
Datavox Communications Corp.

     2.   That the text of the Certificate of Incorporation as amended or
supplemented heretofore is restated hereby to read as herein set forth in full:

     Restated Certificate of Incorporation of Davox Corporation.

     FIRST:    The name of the corporation is:

                               Davox Corporation

     SECOND:   The address of its registered office in the State of Delaware is
Corporation Trust Center, 1209 Orange Street in the City of Wilmington, County
of New Castle.  The name of its registered agent at such address is The
Corporation Trust Company.

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

     FOURTH:   The total number of shares of stock which the corporation shall
have authority to issue is Seven Million Five Hundred Thousand (7,500,000)
shares of Common Stock, and the par value of each of such share is Ten Cents
($.10), amounting in the aggregate to Seven Hundred Fifty Thousand Dollars
($750,000).

     FIFTH:    The Board of Directors is authorized to make, alter or repeal the
by-laws of the corporation.  Election of directors need not be by ballot.

     SIXTH:    The corporation eliminates the personal liability of each member
of its Board of Directors to the corporation or its stockholders for monetary
damages for breach of fiduciary duty as a director, provided that the foregoing
shall not eliminate the liability of a director (i) for any breach of such
director's duty of loyalty to the corporation or its stockholders,
<PAGE>
 
(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 Title 8 of
the Delaware Code of (iv) for any transaction from which such director derived
an improper personal benefit.

     IN WITNESS WHEREOF, the said Davox Corporation has caused this Restated
Certificate of Incorporation to be signed by Daniel A. Hosage, President, and
attested by Timothy C. Maguire, Assistant Secretary, this 26th day of May, 1988.

                                         DAVOX CORPORATION


                                         By:/s/ Daniel A. Hosage
                                            ----------------------------
                                           Daniel A. Hosage, President


Attest:


By:/s/ Timothy C. Maguire
   -----------------------------
   Timothy C. Maguire
   Assistant Secretary
<PAGE>

 
                           CERTIFICATE OF AMENDMENT

                                     TO THE

                              AMENDED AND RESTATED

                          CERTIFICATE OF INCORPORATION

                                       OF

                               DAVOX CORPORATION

     Davox Corporation, a corporation organized and existing under and by virtue
of the General Corporation Law of the State of Delaware (the "Corporation"),
DOES HEREBY CERTIFY:

     FIRST:  That the Board of Directors of the Corporation, at a regularly
scheduled meeting at which all of the members of the Board of Directors were
present and acting throughout, duly adopted a resolution proposing and declaring
advisable an amendment to the Amended and Restated Certificate of Incorporation
of said Corporation.  The resolution setting forth the proposed amendment is as
follows:

RESOLVED:  That it is advisable and in the best interests of the Corporation
           that the Restated Certificate of Incorporation of the Corporation be
           amended to increase the number of authorized shares of the
           Corporation's Common Stock, $.10 par value, to 30,000,000, and that a
           proposal to effectuate such amendment is recommended to the
           stockholders as being in the best interests of the Company.

     SECOND:  That the stockholders of the Corporation have duly approved said
amendment by a vote of the requisite majority of the outstanding capital stock
of said Corporation entitled to vote thereon in accordance with the provisions
of Section 242 of the General Corporation Law of the State of Delaware.

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

                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]
<PAGE>
 
     IN WITNESS WHEREOF, said Davox Corporation has caused this certificate to
be signed by Alphonse M. Lucchese, President, Chief Executive Officer and
Chairman of the Board of Directors, and attested to by Timothy C. Maguire,
Secretary, on this 24th day of April, 1997.

                                         DAVOX CORPORATION


                                         By:  /s/ Alphonse M. Lucchese
                                            --------------------------  
                                              Alphonse M. Lucchese
                                              President

ATTEST:


By:  /s/ Timothy C. Maguire
   --------------------------
     Timothy C. Maguire
     Secretary


[Corporate Seal]