<PAGE>   1
EntreMed, Inc.
Exhibit 3.1(b)



                           CERTIFICATE OF AMENDMENT TO
                              AMENDED AND RESTATED
                          CERTIFICATE OF INCORPORATION
                                       OF
                                 ENTREMED, INC.


        This Certificate of Amendment to the Amended and Restated
Certificate of Incorporation of ENTREMED, INC. (the "Corporation") is
being executed and filed in accordance with Section 242 of the
Delaware General Corporation Law.

        1.  The name of the Corporation is ENTREMED, INC.

        2.  The first paragraph of Article IV of the Corporation's
Amended and Restated Certificate of Incorporation is amended to read as
follows:

                                     "IV.

              The total number of shares of capital stock which the
        Corporation is authorized to issue is Forty Million
        (40,000,000) divided into two classes as follows:"

        3.  Paragraph (A) of Article IV of the Corporation's Amended
and Restated Certificate of Incorporation is amended to read as follows:

              "(A)  Common Stock.  Thirty-Five Million (35,000,000)
        shares of common stock, $.01 par value per share ("Common
        Stock"), the holder of which shall be entitled to one vote for
        each share on all matters required or permitted to be voted on
        by stockholders of the Corporation, and".

        4.  This Certificate of Amendment to Amended and Restated
Certificate of Incorporation and the amendments set forth herein have been
duly adopted by the directors and stockholders of the Corporation in
accordance with the provisions of Section 242 of the Delaware General
Corporation Law.



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IN WITNESS WHEREOF, the Corporation has caused this Certificate of
Amendment to Amended and Restated Certificate of Incorporation to be
executed by the undersigned duly authorized officer of the
Corporation this 31st day of August, 1998.

                               ENTREMED, INC.



                               BY:  /s/ John Holaday
                                   ---------------------
                                   John W. Holaday
                                   President / CEO


/s/ John C. Thomas, Jr.
----------------------------
John C. Thomas, Jr.
Secretary / Treasurer
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EntreMed, Inc.
Exhibit 3.1(b)


                            CERTIFICATE OF CORRECTION
                       FILED TO CORRECT CERTAIN ERRORS IN
              THE CERTIFICATE OF AMENDMENT TO AMENDED AND RESTATED
                          CERTIFICATE OF INCORPORATION
                                       OF
                                 ENTREMED, INC.
                             FILED IN THE OFFICE OF
                       THE SECRETARY OF STATE OF DELAWARE
                                ON APRIL 22, 1996


      ENTREMED, INC., a corporation organized and existing under and by virtue
of the General Corporation Law of the State of Delaware,

      DOES HEREBY CERTIFY AS FOLLOWS:

      1.  The name of the corporation is ENTREMED, INC. (the "Corporation").

      2.  A Certificate of Amendment to Amended and Restated Certificate of
Incorporation was filed by the Corporation with the Secretary of State of the
State of Delaware on April 22, 1996 and said Certificate requires correction as
permitted by Section 103(f) of the General Corporation Law of the State of
Delaware.

      3.  The inaccuracy or defect of said Certificate to be corrected is as
follows: typographic error in Article D Section (4) of said Certificate.

      4.  Article D, Section (4) of said Certificate hereby is corrected to read
as follows:

          "(4) Each and every reference to 'Preferred Stock' as appears in
          Section (B)(X) of Article IV is hereby replaced by the term 'Series
          A Convertible Preferred Stock.'"


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      IN WITNESS WHEREOF, the Corporation has caused this Certificate of
Correction to be executed by the undersigned duly authorized officer of the
Corporation this 26th day of October 1998.

                                          ENTREMED, INC.

                                          By    /s/ R. Nelson Campbell
                                            -----------------------------
                                                R. Nelson Campbell
                                                Chief Financial Officer






<PAGE>   5
EntreMed, Inc.
Exhibit 3.1(b)


                            CERTIFICATE OF CORRECTION
                       FILED TO CORRECT CERTAIN ERRORS IN
              THE CERTIFICATE OF AMENDMENT TO AMENDED AND RESTATED
                          CERTIFICATE OF INCORPORATION
                                       OF
                                 ENTREMED, INC.
                             FILED IN THE OFFICE OF
                       THE SECRETARY OF STATE OF DELAWARE
                              ON SEPTEMBER 4, 1998


      ENTREMED, INC., a corporation organized and existing under and by virtue
of the General Corporation Law of the State of Delaware,

      DOES HEREBY CERTIFY AS FOLLOWS:

      1.  The name of the corporation is ENTREMED, INC. (the "Corporation").

      2.  A Certificate of Amendment to Amended and Restated Certificate of
Incorporation was filed by the Corporation with the Secretary of State of the
State of Delaware on September 4, 1998 and said Certificate requires correction
as permitted by Section 103(f) of the General Corporation Law of the State of
Delaware.

      3.  The inaccuracies or defects of said Certificate to be corrected are as
follows: various typographical errors in Article 3 of said Certificate.

      4.  Article 3 of said Certificate hereby is corrected to read as follows: 

          "3. Paragraph (A) and the first sentence of Paragraph (B) of
      Article IV of the Corporation's Amended and Restated Certificate of
      Incorporation are amended to read as follows:

                  "(A) Common Stock. - Thirty-Five Million (35,000,000)
      shares of common stock, $.01 par value per share ("Common Stock"),
      the holder of which shall be entitled to one vote for each share on
      all matters

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      required or permitted to be voted on by stockholders of the
      Corporation, and

                  "(B) Preferred Stock. - Five Million (5,000,000) shares
      of preferred stock, $1.00 par value per share ("Preferred Stock")."


      IN WITNESS WHEREOF, the Corporation has caused this Certificate of
Correction to be executed by the undersigned duly authorized officer of the
Corporation this 27th day of October 1998.

                                          ENTREMED, INC.

                                          By    /s/ R. Nelson Campbell
                                            ------------------------------
                                                R. Nelson Campbell
                                                Chief Financial Officer