<PAGE>   1
                                                                     Exhibit 3.1

                           CERTIFICATE OF AMENDMENT OF
                              AMENDED AND RESTATED
                          CERTIFICATE OF INCORPORATION
                                       OF
                                 METRICOM, INC.


         METRICOM, INC., a corporation organized and existing under the General
Corporation Law of the State of Delaware (the "Corporation"), does hereby
certify that:

         1. The name of the corporation is Metricom, Inc.

         2. The date on which the Amended and Restated Certificate of
Incorporation was filed with the Secretary of State of the State of Delaware was
May 8, 1992.

         3. The Board of Directors of the Corporation adopted the following
resolutions as required by Section 151 of the General Corporation Law of the
State of Delaware at a meeting duly called and held on May 17, 1996:

                  RESOLVED, that upon the effective date of this Amendment of
the Amended and Restated Certificate of Incorporation, Paragraph A of Article IV
of the Amended and Restated Certificate of Incorporation shall read as follows:

                           "A. This Corporation is authorized to issue two
                  classes of stock to be designated, respectively, "Common
                  Stock" and "Preferred Stock." The total number of shares which
                  the corporation is authorized to issue is Fifty-two million
                  (52,000,000) shares. Fifty million (50,000,000) shares shall
                  be designated Common Stock, each having a par value of one
                  tenth of one cent ($0.001). Two million (2,000,000) shares
                  shall be Preferred Stock, each having a par value of one-tenth
                  of one cent ($0.001)."

         4. Thereafter pursuant to a resolution of the Board of Directors this
Certificate of Amendment was submitted to the stockholders of the corporation
for their approval in accordance with the provisions of Sections 222 and 242 of
the General Corporation Law of the State of Delaware at a meeting duly called
and held on August 7, 1996.

         5. The above Amendment has been duly adopted in accordance with the
provisions of Sections 222 and 242 of the General Corporation Law of the State
of Delaware.

         6. All other provisions of the Amended and Restated Certificate of
Incorporation shall remain in full force and effect.
<PAGE>   2
         IN WITNESS WHEREOF, Metricom, Inc. has caused this certificate to be
signed by its President and Chief Executive Officer, Robert P. Dilworth, and
attested to by its Secretary, William D. Swain, this 13th day of August 1996.


                                       METRICOM, INC.



                                       /s/ Robert P. Dilworth
                                       ----------------------------------------
                                       Robert P. Dilworth
                                       President and Chief Executive Officer
ATTEST:


/s/ William D. Swain
-----------------------------
William D. Swain
Secretary

                                       2.
<PAGE>   3
                              AMENDED AND RESTATED
                          CERTIFICATE OF INCORPORATION
                                       OF
                                 METRICOM, INC.


         ROBERT P. DILWORTH and WILLIAM D. SWAIN hereby certify that:

         1. They are the President and Secretary, respectively, of METRICOM,
INC., a Delaware corporation.

         2. The date of filing of the corporation's original Certificate of
Incorporation was October 24, 1991.

         3. The Amended and Restated Certificate of Incorporation of said
corporation as provided in Exhibit A hereto was duly adopted in accordance with
the provisions of Section 242 and Section 245 of the General Corporation Law of
the State of Delaware by the Board of Directors of the corporation.

         4. Pursuant to Section 245 of the Delaware General Corporation Law,
approval of the stockholders of the corporation has been obtained.

         5. The Amended and Restated Certificate of Incorporation so adopted
reads in full as set forth in Exhibit A attached hereto and hereby incorporated
by reference.

         IN WITNESS WHEREOF, the undersigned have signed this certificate this
8th day of May 1992 and hereby affirm and acknowledge under penalty of perjury
that the filing of this Restated Certificate of Incorporation is the act and
deed of Metricom, Inc.

                                       METRICOM, INC.



                                       /s/ Robert P. Dilworth
                                       ----------------------------------------
                                       Robert P. Dilworth
                                       President and Chief Executive Officer
ATTEST:



/s/ William D. Swain
-------------------------
William D. Swain
Secretary
<PAGE>   4
                              AMENDED AND RESTATED                    EXHIBIT A
                          CERTIFICATE OF INCORPORATION
                                       OF
                                 METRICOM, INC.


                                       I.

         The name of this corporation is Metricom, Inc.

                                       II.

         The address of the registered office of the corporation in the State of
Delaware is 32 Loockermen Square, Suite L-100, City of Dover, County of Kent,
and the name of the registered agent of the corporation in the State of Delaware
at such address is The Prentice-Hall Corporation System, Inc.

                                      III.

         The purpose of this corporation is to engage in any lawful act or
activity for which a corporation may be organized under the General Corporation
Law of the State of Delaware.

         A. The liability of the directors of the Corporation for monetary
damages shall be eliminated to the fullest extent permissible under Delaware
law.

         B. The Corporation is authorized to provide indemnification of agents
(as defined in Section 145 of the Delaware General Corporation Law) for breach
of duty to the Corporation and its stockholders through bylaw provisions,
through agreements with the agents, and/or through stockholder resolutions, or
otherwise, in excess of the indemnification otherwise permitted by Section 145
of the Delaware General Corporation Law.

         C. Any repeal or modification of this Article III shall be prospective
and shall not affect the rights under this Article III in effect at the time of
the alleged occurrence of any act or omission to act giving rise to liability or
indemnification.

                                       IV.

         A. This corporation is authorized to issue two classes of stock to be
designated, respectively, "Common Stock" and "Preferred Stock." The total number
of shares which the corporation is authorized to issue is twenty-two million
(22,000,000) shares. Twenty million (20,000,000) shares shall be Common Stock,
each having a par value of one tenth of one cent ($.001). Two million
(2,000,000) shares shall be Preferred Stock, each having a par value of one
tenth of one cent ($.001).

                                       1.
<PAGE>   5
         B. The Preferred Stock may be issued from time to time in one or more
series. The Board of Directors is hereby authorized, by filing a certificate
pursuant to the Delaware General Corporation Law, to fix or alter from time to
time the designation, powers, preferences and rights of the shares of each such
series and the qualifications, limitations or restrictions thereof, including
without limitation the dividend rights, dividend rate, conversion rights, voting
rights, rights and terms of redemption (including sinking fund provisions),
redemption price or prices, and the liquidation preferences of any wholly
unissued series of Preferred Stock, and to establish from time to time the
number of shares constituting any such series and the designation thereof, or
any of them (a "Preferred Stock Designation"); and to increase or decrease the
number of shares of any series subsequent to the issuance 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 decreased in accordance with
the foregoing sentence, 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.

         C. No share or shares of any series of Preferred Stock acquired by the
Corporation by reason of redemption, purchase, conversion or otherwise shall be
reissued as part of such series, and the Board of Directors is authorized,
pursuant to Section 243 of the Delaware General Corporation Law, to retire any
such share or shares. The retirement of any such share or shares shall not
reduce the total authorized number of shares of Preferred Stock.

                                       V.

         For the management of the business and for the conduct of the affairs
of the corporation, and in further definition, limitation and regulation of the
powers of the corporation, of its directors and of its stockholders or any class
thereof, as the case may be, it is further provided that:

         A. The management of the business and the conduct of the affairs of the
corporation shall be vested in its Board of Directors. The number of directors
which shall constitute the whole Board of Directors shall be fixed exclusively
by one or more resolutions adopted from time to time by the Board of Directors.

         The directors shall be divided into three classes designated as Class
I, Class II and Class III, respectively. Directors shall be assigned to each
class in accordance with a resolution or resolutions adopted by the Board of
Directors. At the first annual meeting of stockholders following the closing of
the Initial Public Offering, the term of office of the Class I directors shall
expire and Class I directors shall be elected for a full term of three years. At
the second annual meeting of stockholders following the closing of the Initial
Public Offering, the term of office of the Class II directors shall expire and
Class II directors shall be elected for a full term of three years. At the third
annual meeting of stockholders following the closing of the Initial Public
Offering, the term of office of the Class III directors shall expire and Class
III directors shall be elected for a full term of three years. At each
succeeding annual meeting of stockholders, directors shall be elected for a full
term of three years to succeed the directors of the class whose terms expire at
such annual meeting.

                                       2.
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         Notwithstanding the foregoing provisions of this Article, each director
shall serve until his successor is duly elected and qualified or until his
death, resignation or removal. No decrease in the number of directors
constituting the Board of Directors shall shorten the term of any incumbent
director.

         Any vacancies on the Board of Directors resulting from death,
resignation, disqualification, removal or other causes shall be filled by either
(i) the affirmative vote of the holders of a majority of the voting power of the
then-outstanding shares of voting stock of the corporation entitled to vote
generally in the election of directors (the "Voting Stock") voting together as a
single class; or (ii) by the affirmative vote of a majority of the remaining
directors then in office, even though less than a quorum of the Board of
Directors. Newly created directorships resulting from any increase in the number
of directors shall, unless the Board of Directors determines by resolution that
any such newly created directorship shall be filled by the stockholders, be
filled only by the affirmative vote of the directors then in office, even though
less than a quorum of the Board of Directors. Any director elected in accordance
with the preceding sentence shall hold office for the remainder of the full term
of the class of directors in which the new directorship was created or the
vacancy occurred and until such director's successor shall have been elected and
qualified.

         B. The Bylaws may be altered or amended or new Bylaws adopted by the
affirmative vote of at least sixty-six and two-thirds percent (66-2/3%) of the
voting power of all of the then-outstanding shares of the Voting Stock. In
furtherance and not in limitation of the power conferred by statute, the Board
of Directors is expressly authorized to adopt, amend, supplement or repeal the
Bylaws.

         C. The directors of the corporation need not be elected by written
ballot unless the Bylaws so provide.

         D. No action shall be taken by the stockholders of the corporation
except at an annual or special meeting of stockholders called in accordance with
the Bylaws and no action shall be taken by the stockholders by written consent.

         E. Advance notice of stockholder nominations for the election of
directors and of business to be brought by stockholders before any meeting of
the stockholders of the corporation shall be given in the manner provided in the
Bylaws of the corporation.

         F. Any director, or the entire Board of Directors, may be removed from
office at any time (i) with cause by the affirmative vote of the holders of at
least a majority of the voting power of all of the then-outstanding shares of
the Voting Stock, voting together as a single class; or (ii) without cause by
the affirmative vote of the holders of at least sixty-six and two-thirds percent
(66-2/3%) of the voting power of all of the then-outstanding shares of the
Voting Stock.

                                       3.
<PAGE>   7
                                       VI.

         Notwithstanding any other provisions of this Certificate of
Incorporation or any provision of law which might otherwise permit a lesser vote
or no vote, but in addition to any affirmative vote of the holders of any
particular class or series of the Voting Stock required by law, this Certificate
of Incorporation or any Preferred Stock Designation, the affirmative vote of the
holders of at least sixty-six and two-thirds percent (66-2/3%) of the voting
power of all of the then-outstanding shares of the Voting Stock, voting together
as a single class, shall be required to alter, amend or repeal Article V or
Article VIII.

                                      VII.

         The corporation is to have perpetual existence.

                                      VIII.

         The corporation reserves the right to amend, alter, change or repeal
any provision contained in this Certificate of Incorporation, in the manner now
or hereafter prescribed by statute, except as provided in Article VI of this
Certificate, and all rights conferred upon the stockholders herein are granted
subject to this right.

                                       4.