<PAGE>   1
                                                                     EXHIBIT 3.A


                                    RESTATED

                          CERTIFICATE OF INCORPORATION

                                       OF

                          EL PASO NATURAL GAS COMPANY


         E1 Paso Natural Gas Company, a corporation organized and existing
under the General Corporation Law of the State of Delaware, does hereby
certify:

         1.      The original Certificate of Incorporation was filed with the
Secretary of State on November 28, 1928.  The name under which it was
originally incorporated is El Paso Natural Gas Company.

         2.      The following Restated Certificate of Incorporation was duly
proposed by the corporation's Board of Directors pursuant to the applicable
provisions of Section 245 of the General Corporation Law of the State of
Delaware.  The following Restated Certificate of Incorporation only restates and
integrates and does not further amend the provisions of the corporation's
certificate of incorporation as heretofore amended and supplemented, and there
is no discrepancy between those provisions and the following Restated
Certificate of Incorporation, except for such provisions as are expressly
permitted to be omitted by Section 245 of the General Corporation law of the
State of Delaware.


                                ARTICLE 1.  NAME

         The name of this corporation is EL PASO NATURAL GAS COMPANY.


                    ARTICLE 2.  REGISTERED OFFICE AND AGENT

         The address of the registered office of this corporation is
Corporation Trust Center, 1209 Orange Street, City of Wilmington, County of New
Castle, State of Delaware 19801, and the name of its registered agent at such
address is The Corporation Trust Company.


                              ARTICLE 3.  PURPOSES

         The purpose of this corporation is to engage in any lawful act or
activity for which corporations may be organized under the General Corporation
Law of the State of Delaware.
<PAGE>   2
                               ARTICLE 4.  SHARES

         The total number of authorized shares of all classes of stock of this
corporation shall consist of 1,000 shares of common stock having a par value of
$1.00 per share and 1,000,000 shares of preferred stock having a par value of
$0.01 per share.  Authority is hereby expressly granted to the Board of
Directors to fix by resolution or resolutions any of the designations and the
powers, preferences and rights, and the qualifications, limitations or
restrictions which are permitted by the General Corporation Law of the State of
Delaware in respect of any class or classes of stock or any series of any class
of stock of the corporation.

                              ARTICLE 5.  BY-LAWS

         The Board of Directors shall have the power to adopt, amend or repeal
the By-laws of this corporation, subject to the power of the stockholders to
amend or repeal such By-laws.  The stockholders having voting power shall also
have the power to adopt, amend or repeal the By-laws of this corporation.

                       ARTICLE 6.  ELECTION OF DIRECTORS

         Except as may be otherwise required by the By-laws, written ballots
are not required in the election of Directors.

                         ARTICLE 7.  PREEMPTIVE RIGHTS

         Preemptive rights shall not exist with respect to shares of stock or
securities convertible into shares of stock of this corporation.

                         ARTICLE 8.  CUMULATIVE VOTING

         The right to cumulate votes in the election of Directors shall not
exist with respect to shares of stock of this corporation.

        ARTICLE 9.  AMENDMENTS TO RESTATED CERTIFICATE OF INCORPORATION

         This corporation reserves the right to amend or repeal any of the
provisions contained in this Restated Certificate of Incorporation in any
manner now or hereafter permitted by law, and the rights of the stockholders of
this corporation are granted subject to this reservation.




                                     -2-
<PAGE>   3
                 ARTICLE 10.  LIMITATION OF DIRECTOR LIABILITY

         To the full extent that the General Corporation Law of the State of
Delaware, as it exists on the date hereof or may hereafter be amended, permits
the limitation or elimination of the liability of Directors, a Director of this
corporation shall not be liable to this corporation or its stockholders for
monetary damages for breach of fiduciary duty as a Director.  Any amendment to
or repeal of this Article 10 shall not adversely affect any right or protection
of a Director of this corporation for or with respect to any acts or omissions
of such Director occurring prior to such amendment or repeal.

             ARTICLE 11.  ACTION BY STOCKHOLDERS WITHOUT A MEETING

         Any action by the stockholders of this corporation shall be taken at a
meeting of stockholders and no action may be taken by written consent of
stockholders entitled to vote on such action.

                    ARTICLE 12.  SPECIAL VOTING REQUIREMENTS

         In addition to any affirmative vote required by law, by this Restated
Certificate of Incorporation, by any agreement with any national securities
exchange, or as may be otherwise required, any "Business Combination" (as
hereinafter defined) involving this corporation shall be subject to approval in
the manner set forth in this Article 12.

         12.1 Definitions.

         For the purposes of this Article 12:

                 (a)      "Affiliate" and "beneficial owner" are used herein as
         defined in Rule 12b-2 and Rule 13d-3, respectively, under the
         Securities Exchange Act of 1934 as in effect on January 1, 1992 (the
         "1934 Act").  The term "Affiliate" as used herein shall exclude this
         corporation, but shall include the definition of "Associate" as
         contained in said Rule 12b-2.

                 (b)      An "Interested Stockholder" is a person other than
         (i) the corporation or (ii) Burlington Resources Inc., a Delaware
         corporation ("BRI"), as long as BRI continues to own at least a
         majority of the stock of this corporation entitled to vote for the
         election of Directors ("Voting Stock") and there has been no Change in
         Control of BRI since January 1, 1992, who is (A) the beneficial owner
         of ten percent or more of the Voting Stock or (B) an Affiliate of this
         corporation which (1) at any time within a two-year period prior to
         the record date for the vote on a Business Combination was the
         beneficial owner of ten percent or more of the Voting Stock, or (2) at
         the completion of the Business Combination will be the beneficial
         owner of ten percent or more of the Voting Stock.




                                     -3-
<PAGE>   4
                 (c)      A "Person" is a natural person or a legal entity of
         any kind, together with any Affiliate of such person or entity, or any
         person or entity with whom such person, entity or any Affiliate has
         any agreement or understanding relating to acquiring, voting or
         holding Voting Stock.

                 (d)      A "Disinterested Director" is a member of the Board
         of Directors of this corporation (other than the Interested
         Stockholder) who was a Director prior to the time the Interested
         Stockholder became an Interested Stockholder, or any Director who was
         recommended for election by the Disinterested Directors.  Any action
         to be taken by the Disinterested Directors shall require the
         affirmative vote of at least two-thirds of the Disinterested
         Directors.

                 (e)      A "Business Combination" is (i) a merger or
         consolidation of this corporation or any of its subsidiaries with an
         Interested Stockholder; (ii) the sale, lease, exchange, pledge,
         transfer or other disposition (A) by this corporation or any of its
         subsidiaries of all or a Substantial Part of the corporation's Assets
         to an Interested Stockholder, or (B) by an Interested Stockholder of
         any of its assets, except in the ordinary course of business, to this
         corporation or any of its subsidiaries; (iii) the issuance of stock or
         other securities of this corporation or any of its subsidiaries to an
         Interested Stockholder, other than on a pro rata basis to all holders
         of Voting Stock of the same class held by the Interested Stockholder
         pursuant to a stock spilt, stock dividend or distribution of warrants
         or rights; (iv) the adoption of any plan or proposal for the
         liquidation or dissolution of this corporation proposed by or on
         behalf of an Interested Stockholder; (v) any reclassification of
         securities, recapitalization, merger or consolidation or other
         transaction which has the effect, directly or indirectly, of
         increasing the proportionate share of any Voting Stock beneficially
         owned by an Interested Stockholder; or (vi) any agreement, contract or
         other arrangement providing for any of the foregoing transactions.

                 (f)      A "Substantial Part of the corporation's Assets"
         shall mean assets of this corporation or any of its subsidiaries in an
         amount equal to twenty percent or more of the fair market value, as
         determined by the Disinterested Directors, of the total consolidated
         assets of this corporation and its subsidiaries taken as a whole as of
         the end of its most recent fiscal year ended prior to the time the
         determination is made.

                 (g)      A "Change in Control" shall be deemed to occur (i) if
         any Person is or becomes the "beneficial owner" (as defined in Rule
         13d-3 of the 1934 Act), directly or indirectly, of securities of BRI
         representing twenty percent or more of the stock of BRI entitled to
         vote for Directors of BRI, (ii) upon the first purchase of BRI's
         common stock pursuant to a tender or exchange offer (other than a
         tender or exchange offer made by BRI), (iii) upon the approval by
         BRI's stockholders of a merger or consolidation, a sale or disposition
         of all or substantially all of BRI's assets or a plan of liquidation
         or dissolution of BRI, or (iv) if, during any period of two
         consecutive years, individuals who at the beginning of such period
         constitute the BRI Board of Directors cease for any reason to
         constitute at least a majority thereof, unless the election or
         nomination of the election by




                                     -4-
<PAGE>   5
         BRI's stockholders of each new Director was approved by a vote of at
         least  two-thirds of the Directors then still in office who were
         Directors at the beginning of the period.

         12.2  Vote Required for Business Combinations.

         The affirmative vote of not less than fifty-one percent of the Voting
Stock, excluding the Voting Stock of an Interested Stockholder who is a party
to the Business Combination, shall be required for the adoption or
authorization of a Business Combination, unless the Disinterested Directors
determine that:

                 (a)      The Interested Stockholder is the beneficial owner of
         not less than eighty percent of the Voting Stock and has declared its
         intention to vote in favor of or to approve such Business Combination;
         or

                 (b)      (i) The fair market value of the consideration per
         share to be received or retained by the holders of each class or
         series of stock of this corporation in a Business Combination is equal
         to or greater than the consideration per share (including brokerage
         commissions and soliciting dealer's fees) paid by such Interested
         Stockholder in acquiring the largest number of shares of such class of
         stock previously acquired in any one transaction or series of related
         transactions, whether before or after the Interested Stockholder
         became an Interested Stockholder and (ii) the Interested Stockholder
         shall not have received the benefit, directly or indirectly (except
         proportionately as a stockholder), of any loans, advances, guarantees,
         pledges or other financial assistance provided by this corporation,
         whether in anticipation of or in connection with such Business
         Combination or otherwise.

         12.3  Information Requirements.

         In the event any vote of holders of Voting Stock is required for the
adoption or approval of any Business Combination, a proxy or information
statement describing the Business Combination and complying with the
requirements of the 1934 Act shall be mailed at a date determined by the
Disinterested Directors to all stockholders of this corporation whether or not
such statement is required under the 1934 Act.  The statement shall contain any
recommendations as to the advisabi1ity of the Business Combination which the
Disinterested Directors, or any of them, may choose to state and, if deemed
advisable by the Disinterested Directors, an opinion of an investment banking
firm as to the fairness of the terms of such Business Combination.  Such firm
shall be selected by the Disinterested Directors and be paid a fee for its
services by this corporation as approved by the Disinterested Directors.

         12.4  Amendment.

         No amendment to this Restated Certificate of Incorporation shall
amend, alter, change or repeal any of the provisions of Article 11 or of this
Article 12 unless such amendment shall receive the affirmative vote of not less
than fifty-one percent of the Voting Stock, excluding the Voting Stock of any
Interested Stockholder as defined in Section 12.1 of this Article 12.




                                     -5-
<PAGE>   6
               ARTICLE 13. VOTE OF STOCKHOLDERS OF EL PASO ENERGY
                CORPORATION REQUIRED TO APPROVE CERTAIN ACTIONS

         Any act or transaction by or involving this corporation that requires
for its adoption under the General Corporation Law of the State of Delaware or
this Restated Certificate of Incorporation the approval of the stockholders of
this corporation shall, pursuant to Section 251(g) of the General Corporation
Law of the State of Delaware, require, in addition, the approval of the
stockholders of El Paso Energy Corporation, a Delaware corporation, or any
successor thereto by merger, by the same vote that is required by the General
Corporation Law of the State of Delaware and/or the Restated Certificate of
Incorporation of this corporation.

         IN WITNESS WHEREOF, the undersigned has executed this document and
affirms, under penalties of perjury, that the statements herein are true and
that this instrument is the act and deed of El Paso Natural Gas Company as of
this 3rd day of August  1998.


                                        EL PASO NATURAL GAS COMPANY



                                                /s/ H. Brent Austin
                                        ----------------------------------------
                                                    H. Brent Austin
                                           Executive Vice President and Chief
                                               Financial Executive Officer



Attest:

       /s/ David L. Siddall
--------------------------------------
           David L. Siddall
         Corporate Secretary




                                     -6-

<PAGE>   7
                          EL PASO NATURAL GAS COMPANY

     CERTIFICATE OF DESIGNATION, PREFERENCES AND RIGHTS OF PREFERRED STOCK
                    BY RESOLUTION OF THE BOARD OF DIRECTORS
                       PROVIDING FOR AN ISSUE OF 500,000
                      SHARES OF PREFERRED STOCK DESIGNATED
                              "8% PREFERRED STOCK"

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

         I, Kelly J. Jameson, Assistant Secretary of El Paso Natural Gas Company
(hereinafter referred to as the "Corporation"), a corporation organized and 
existing under the General Corporation Law of the State of Delaware, in 
accordance with the provisions of Section 151 thereof, DO HEREBY CERTIFY:

         That pursuant to authority conferred upon the Board of Directors by 
the Certificate of Incorporation, as amended, of said Corporation, the Board of 
Directors, by unanimous written consent, pursuant to Section 141(f) of the 
General Corporation Law of the State of Delaware, dated as of December 30, 
1998, adopted a resolution providing for the issuance of a series of Preferred 
Stock, to be designated "8% Preferred Stock," which resolution is as follows:

                  RESOLVED, that pursuant to the authority vested in the Board
         of Directors of the Corporation by the Certificate of Incorporation, as
         amended (as such may be further amended from time to time, the
         "Certificate of Incorporation"), a series of Preferred Stock, par value
         $0.01 per share, of the Corporation (the "Preferred Stock") be, and
         hereby is, created to be designated "8% Preferred Stock" (hereinafter
         referred to as the "8% Preferred Stock"), consisting of 500,000 shares,
         and the designations, powers, preferences and relative and other
         special rights and the qualifications, limitations and restrictions of
         the 8% Preferred Stock are hereby fixed and stated to be as follows
         (all terms used herein that are defined in the Certificate of
         Incorporation shall be deemed to have the meanings provided therein):

                  SECTION 1. Dividends. (a) The dividend rate on the 8%
         Preferred Stock shall be 8% of $700 per share of Preferred Stock per
         annum. Dividends on shares of the 8% Preferred Stock shall be
         cumulative and shall accrue from the date of issuance of such shares,
         whether or not declared by the Board of Directors of the Corporation
         (or a duly authorized committee thereof). Accrued but unpaid dividends
         shall not bear interest.
<PAGE>   8
                  (b) Dividends on the 8% Preferred Stock shall be payable,
         when, as, and if declared by the Board of Directors of the Corporation
         (or a duly authorized committee thereof) out of assets legally
         available therefor, annually on the last day of November in each year
         (each, a "Dividend Payment Date"), with the first dividend payment date
         being the next Dividend Payment Date following the date of issuance.
         Dividends on each Dividend Payment Date will be payable to holders of
         record of the 8% Preferred Stock as they appear on the records of the
         Corporation on a record date, not more than 60 days preceding such
         Dividend Payment Date, fixed for such purpose by the Board of Directors
         (or a duly authorized committee thereof) in advance of such Dividend
         Payment Date. Accrued dividends not paid on a Dividend Payment Date may
         be declared and paid at any time, without reference to any regular
         Dividend Payment Date, to the holders of record on such record date,
         not more than 60 days preceding the payment date thereof, as may be
         fixed by the Board of Directors (or a duly authorized committee
         thereof). Dividends payable on shares of 8% Preferred Stock for the
         initial dividend period following issuance of such shares or any other
         dividend period shorter than a year shall be computed on the basis of a
         360-day year of twelve 30-day months. The 8% Preferred Stock shall rank
         on a parity with each other series of Preferred Stock as to the payment
         of dividends, except to the extent otherwise provided in the resolution
         or resolutions of the Board of Directors of the Corporation fixing 
         the designations and the powers, preferences, and rights, and the
         qualifications, limitations, and restrictions in respect of such other
         series of Preferred Stock.

                  SECTION 2. Voting. The 8% Preferred Stock shall not have any
         voting rights except as required by law or the Certificate of
         Incorporation.

                  SECTION 3. Redemption. (a) At any time or from time to time,
         on or after January 1, 2003, the shares of the 8% Preferred Stock shall
         be redeemable at the option of the corporation (by resolution of the
         Board of Directors or a duly authorized committee thereof), in whole or
         in part, out of funds legally available therefor, at a redemption price
         equal to $700.00 per share, plus an amount equal to all accrued and
         unpaid dividends, if any, to but excluding the date fixed for
         redemption. If fewer than all outstanding shares of 8% Preferred Stock
         are to be redeemed, the Corporation will select those shares to be
         redeemed pro rata, by lot, or by a substantially equivalent method.

                  (b) Notice of redemption pursuant to paragraph (a) of this
         Section 3 shall be given by mail, not less than 30 days prior to the
         date fixed for redemption, to each record holder of the shares of 8%
         Preferred Stock to be redeemed at the address of such holder on the
         records of the
<PAGE>   9
         Corporation. If a notice of redemption has been given pursuant to this
         subsection (b) and if, on or before the date fixed for redemption, the
         funds necessary for such redemption shall have been irrevocably
         deposited or set aside by the Corporation, separate and apart from its
         other funds, to pay the redemption price to the holders of the shares
         of 8% Preferred Stock so called for redemption upon surrender of the
         certificates therefor, then, notwithstanding that any certificates for
         such shares have not been surrendered for cancellation, from and after
         the date fixed for redemption, dividends on the shares of 8% Preferred
         Stock so called for redemption will cease to accrue, such shares will
         no longer be deemed outstanding, and all rights of the holders thereof
         as stockholders of the Corporation (except the right to receive payment
         of the redemption price) will cease. Subject to applicable escheat and
         similar abandoned property laws, any moneys so deposited or set aside
         by the Corporation for such redemption and unclaimed at the end of the
         six months from the date fixed for redemption shall revert to the
         general funds of the Corporation, after which reversion the holders of
         such shares so called for redemption shall look only to the general
         funds of the Corporation for payment of the amounts payable upon such
         redemption. Any interest accrued on funds so deposited or set aside
         shall be paid to the Corporation from time to time.

                 SECTION 4. Liquidation Rights. (a) The shares of 8% Preferred 
         Stock shall rank, as to distributions upon dissolution, liquidation, 
         and winding up of the Corporation, prior to the shares of Common Stock 
         and on parity with each other series of Preferred Stock, except to the 
         extent otherwise provided in the resolution or resolutions of the 
         Board of Directors of the Corporation on fixing the designations and 
         the powers, preferences, and rights, and the qualifications, 
         limitations, and restrictions in respect of such other series of 
         Preferred Stock. Subject to subsection (b) of this Section 4, the 
         amount that the holders of 8% Preferred Stock shall be entitled to 
         receive in the event of any dissolution, liquidation, or winding up of 
         the affairs of the Corporation, whether voluntary or involuntary, 
         shall be $700.00 per share, plus an amount equal to all accrued and 
         unpaid dividends, if any, to the date of dissolution or liquidation. 
         After such amount is paid in full, no further distributions or 
         payments shall be made in respect of shares of 8% Preferred Stock, 
         such shares of 8% Preferred Stock shall no longer be deemed to be 
         outstanding or be entitled to any powers, preferences, rights, or 
         privileges, and certificates representing such shares of 8% Preferred 
         Stock shall be surrendered for cancellation to the Corporation.

                 (b) In the event of any dissolution, liquidation, or winding 
         up of the Corporation, then, before any distribution or payment shall 
         be made to the holders of Common Stock or any other class or series of 
         stock of the
<PAGE>   10
         Corporation ranking junior to the 8% Preferred Stock with respect to
         distributions upon dissolution, liquidation, or winding up, the holders
         of the 8% Preferred Stock (subject to the rights of the holders of any
         class or series of stock ranking prior to the 8% Preferred Stock with
         respect to distributions upon dissolution, liquidation, or winding up)
         shall be entitled to be paid in full the amounts set forth in
         subsection (a) of this Section 4. After such payment shall have been
         made in full to the holders of the 8% Preferred Stock, the remaining
         assets and funds of the Corporation shall be distributed to the holders
         of the stock of the Corporation ranking junior to the 8% Preferred
         Stock with respect to distributions upon dissolution, liquidation, or
         winding up according to their respective rights. In the event that the
         assets of the Corporation available for distribution to the holders of
         8% Preferred Stock shall not be sufficient to pay in full the
         preferential payment herein required to be paid to the holders of
         shares of 8% Preferred Stock and to pay in full the liquidation
         preference on all other shares of stock of the Corporation ranking on
         parity with the 8% Preferred Stock with respect to distributions upon
         dissolution, liquidation, and winding up of the Corporation, then such
         assets shall be distributed to the holders of shares of 8% Preferred
         Stock and any such other parity stock ratably in proportion to the full
         amounts to which they otherwise would be respectively entitled if all
         amounts payable thereon were paid in full.

                  SECTION 5. Maturity. Unless otherwise redeemed as provided
         herein, the term of the 8% Preferred Stock shall be perpetual.

         IN WITNESS WHEREOF, said El Paso Natural Gas Company has caused this
Certificate of Designation, Preferences and Rights of Preferred Stock to be
signed by Kelly J. Jameson, as Assistant Secretary, this 30th day of December
1998.

                                            EL PASO NATURAL GAS COMPANY


                                            By: /s/ Kelly J. Jameson
                                               -----------------------------
                                                    Kelly J. Jameson
                                                    Assistant Secretary