<PAGE>   1


                                                                     EXHIBIT 4.6



                            CERTIFICATE OF AMENDMENT

                                       OF

                          CERTIFICATE OF INCORPORATION

                                       OF

                         ARCH COMMUNICATIONS GROUP, INC.



     Arch Communications Group, Inc. (hereinafter called the "Corporation"),
organized and existing under and by virtue of the General Corporation Law of the
State of Delaware, does hereby certify as follows:

     At a duly convened meeting of the Board of Directors of the Corporation, a
resolution was duly adopted pursuant to Section 242 of the General Corporation
Law of the State of Delaware setting forth amendments to the Restated
Certificate of Incorporation of the Corporation, as amended by a Certificate of
Designation dated October 13, 1995 stating the designation and number of shares,
and fixing the relative rights, preferences and limitations, of the
Corporation's Series B Junior Participating Preferred Stock (the "Series B
Certificate of Designation") and a Certificate of Designation dated June 29,
1998 stating the designation and number of shares, and fixing the relative
rights, preferences and limitations, of the Corporation's Series C Convertible
Preferred Stock (as so amended, the "Restated Certificate of Incorporation"),
and declaring such amendments to be advisable. The stockholders of the
Corporation duly approved said proposed amendments in accordance with Section
242 of the General Corporation Law of the State of Delaware at a duly convened
meeting of stockholders. The resolutions setting forth the amendments are as
follows:

RESOLVED:      That Article FOURTH of the Restated Certificate of
               Incorporation of the Corporation, as previously amended,
               be and hereby is further amended by deleting paragraph (a)
               of said Article FOURTH and inserting in lieu thereof the
               following:



               (a) The aggregate number of shares of all classes of stock which
               the Corporation shall have authority to issue is 375,000,000
               shares, consisting of (i) 300,000,000 shares of Common Stock,
               $.01 par value per share ("Common Stock"), (ii) 65,000,000 shares
               of Class B Common Stock, $.01 par value per







<PAGE>   2

               share ("Class B Common Stock"), and (iii) 10,000,000 shares of
               preferred stock, $.01 par value per share ("Preferred Stock"), of
               which 300,000 shares have been designated as Series B Junior
               Participating Preferred Stock, $.01 par value per share, 250,000
               shares have been designated as Series C Convertible Preferred
               Stock, $.01 par value per share, and 9,450,000 shares remain
               available for future designation and issuance in accordance with
               the General Corporation Law of the State of Delaware.

FURTHER
RESOLVED:      That Article FOURTH of the Restated Certificate of Incorporation
               be and hereby is amended by deleting subparagraph (b)(i) of said
               Article FOURTH and inserting in lieu thereof the following:

               (i) Common Stock and Class B Common Stock.

                    (A) Subject to the provisions of any series of Preferred
               Stock which may at the time be outstanding, the holders of Common
               Stock and Class B Common Stock shall be entitled to receive, when
               and as declared from time to time by the Board of Directors out
               of any funds legally available for the purpose, such dividends as
               may be declared from time to time by the Board of Directors. When
               and as dividends are declared thereon, whether payable in cash,
               property or securities of the Corporation, each holder of Common
               Stock or Class B Common Stock will be entitled to participate in
               such dividends ratably on a per share basis. In the event of any
               liquidation, dissolution or winding up of the Corporation,
               whether voluntary or involuntary, or upon the distribution of its
               assets, after the payment in full or the setting apart for
               payment of such preferential amounts, if any, to which the
               holders of Preferred Stock at the time outstanding shall be
               entitled, the remaining assets of the Corporation available for
               payment and distribution to stockholders shall, subject to any
               participating or similar rights of any series of Preferred Stock
               at the time outstanding, be distributed ratably among the holders
               of Common Stock and Class B Common Stock at the time outstanding
               on a per share basis. Shares of Common Stock shall have no
               preference, conversion, exchange, preemptive or other similar
               rights. Shares of Class B Common Stock shall have no preference,
               exchange, preemptive right or other similar rights, shall be
               identical in all respects to shares of Common Stock except as set
               forth in subparagraphs (B), (C) and (D) below, and shall have no
               conversion rights except as set forth in subparagraphs (C) and
               (D) below.

                    (B) Except as otherwise required by the General Corporation
               Law of the State of Delaware or this Certificate of
               Incorporation, on all matters to be voted on by the Corporation's
               stockholders, the Common Stock will be entitled to one vote per
               share. Except as otherwise required by the General





<PAGE>   3

               Corporation Law of the State of Delaware or this Certificate of
               Incorporation, the Class B Common Stock shall not be entitled to
               vote with respect to the election of directors and shall be
               entitled to 1/100th vote per share on all other matters to be
               voted on by the Corporation's stockholders. Except as otherwise
               required by the General Corporation Law of the State of Delaware
               or this Certificate of Incorporation, the Common Stock, the Class
               B Common Stock and the Preferred Stock shall vote as a single
               class with respect to all matters as to which such shares are
               entitled to vote.

                    (C) Upon any transfer of shares of Class B Common Stock to a
               person or entity other than (i) any person or entity who received
               Class B Common Stock pursuant to Section 4.3(C) of the Debtor's
               Third Amended Joint Plan of Reorganization dated November 30,
               1998 as filed by MobileMedia Corporation, MobileMedia
               Communications, Inc. and MobileMedia Communications, Inc.'s
               direct and indirect subsidiaries with the United States
               Bankruptcy Court for the District of Delaware, Case No. 97-174
               (PJW), including the Rights Offering as defined therein (the
               "Initial Distributees"), (ii) any other person or entity who,
               when taken together with any of the Initial Distributees, would
               constitute a "person" or "group" as such terms are used in
               Sections 13(d) and 14(d) of the Securities Exchange Act of 1934,
               as amended, or (iii) any "affiliate" (as such term is defined in
               Rule 405 promulgated under the Securities Act of 1933, as
               amended) of any of them (collectively, the "Class B Holders"),
               such transferred shares shall automatically convert into an
               identical number of shares of Common Stock without any action on
               the part of any person or entity (except as follows). The Class B
               Holder transferring such shares shall surrender to the
               Corporation at its principal office the share certificate or
               certificates evidencing all such shares of Class B Common Stock
               being transferred together with a certificate (a "Transfer
               Certificate") (i) stating the number of shares of Class B Common
               Stock being transferred to such transferee and (ii) stating that,
               to the knowledge of such Class B Holder, after due inquiry, such
               transferee is not a Class B Holder. Promptly after the delivery
               of such share certificate or certificates, together with such
               Transfer Certificate, the Corporation shall (i) cause to be
               issued in the name of the transferee identified in the Transfer
               Certificate and delivered to such Class B Holder, or to such
               person as directed by his or its written order, a share
               certificate or certificates for the number of shares of Common
               Stock equal to the number of shares of Class B Common Stock being
               transferred to such transferee and (ii) cause to be issued in the
               name of such Class B Holder and delivered to such Class B Holder
               a share certificate or certificates evidencing the number of
               shares, if any, of Class B Common Stock evidenced by the share
               certificate or certificate(s) surrendered to the Corporation not
               being so transferred. Upon such transfer, all rights with respect
               to the Class B Common Stock so converted will terminate, except
               only the rights of the holders thereof, upon surrender of their
               share certificate or certificates therefor, to receive
               certificates registered in the name of its transferee for the
               number of


<PAGE>   4


               shares of Common Stock into which such Class B Common Stock has
               been converted, and payment of any declared but unpaid dividends
               thereon.

                    (D) Any Class B Holder may, at any time and from time to
               time by surrendering to the Corporation at its principal office a
               share certificate or certificates for shares of Class B Common
               Stock together with a certificate (a "Conversion Certificate")
               stating that such Class B Holder has transferred shares of Common
               Stock (in an amount set forth in such Conversion Certificate) to
               a transferee that, to the knowledge of such Class B Holder, after
               due inquiry, is not a Class B Holder, request that the
               Corporation exchange shares of Common Stock, on a one-for-one
               basis, for a number of shares of Class B Common Stock not greater
               than the number of shares of Common Stock set forth in such
               Conversion Certificate. The Corporation shall, upon receipt of
               such certificate or certificates and the Conversion Certificate
               in a form the Corporation deems appropriate, issue an equal
               number of shares of Common Stock in exchange for such number of
               shares of Class B Common Stock set forth in any Conversion
               Certificate.

                    (E) All certificates evidencing shares of Class B Common
               Stock which are surrendered for transfer and conversion in
               accordance with the provisions of subparagraph (C) above, or as
               accepted for conversion in accordance with the provisions of
               subparagraph (D) above, shall, from and after the presentation
               thereof together with any other documentation required hereunder,
               be deemed to have been retired and cancelled and the shares of
               Class B Common Stock represented thereby converted into Common
               Stock for all purposes. The Corporation may thereafter take such
               appropriate action (without the need for stockholder action) as
               may be necessary to reduce the authorized Class B Common Stock
               accordingly.

FURTHER
RESOLVED:      That Article FOURTH of the Restated Certificate of Incorporation
               be and hereby is amended by deleting subparagraph (b)(ii) of
               said Article FOURTH.



FURTHER
RESOLVED:      That the Series B Certificate of Designations be and hereby is
               amended by deleting Section 1 thereof and inserting in lieu
               thereof the following:

               Section 1. DESIGNATION AND AMOUNT. The shares of such series
               shall be designated as "Series B Junior Participating Preferred
               Stock" (the "Series B Preferred Stock") and the number of shares
               constituting the Series B Preferred Stock shall be 300,000. Such
               number of shares may be increased or decreased by resolution of
               the Board of Directors; provided that no decrease shall reduce
               the number of shares of Series B Preferred Stock to a number less
               than the number of shares then outstanding plus the number of
               shares reserved for



<PAGE>   5


               issuance upon the exercise of outstanding options, rights or
               warrants or upon the conversion of any outstanding securities
               issued by the Corporation convertible into Series B Preferred
               Stock.



     IN WITNESS WHEREOF, the Corporation has caused its corporate seal to be
affixed hereto and this Certificate of Amendment to be signed by its Chairman
and Chief Executive Officer and attested by its Secretary this 27th day of May,
1999.


                                      ARCH COMMUNICATIONS GROUP, INC.


                                          /s/ C. Edward Baker, Jr.
                                      By:---------------------------------
                                      C. Edward Baker, Jr.
                                      Chairman and Chief Executive Officer



Dated:  May 27, 1999

ATTEST:

/S/ GARRY B. WATZKE
------------------------------
Garry B. Watzke
Secretary