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                                                                    Exhibit 31.1

             CERTIFICATION OF PRESIDENT AND CHIEF EXECUTIVE OFFICER

I, Gregory E. A. Morrison, certify that:

   1.   I have reviewed this report on Form 10-K of Platinum Underwriters
        Holdings, Ltd. (the "registrant");

   2.   Based on my knowledge, this report does not contain any untrue statement
        of a material fact or omit to state a material fact necessary to make
        the statements made, in light of the circumstances under which such
        statements were made, not misleading with respect to the period covered
        by this report;

   3.   Based on my knowledge, the financial statements, and other financial
        information included in this report, fairly present in all material
        respects the financial condition, results of operations and cash flows
        of the registrant as of, and for, the periods presented in this report;

   4.   The registrant's other certifying officer and I are responsible for
        establishing and maintaining disclosure controls and procedures (as
        defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) for the
        registrant and have:

         a)   Designed such disclosure controls and procedures, or caused such
              disclosure controls and procedures to be designed under our
              supervision, to ensure that material information relating to the
              registrant, including its consolidated subsidiaries, is made known
              to us by others within those entities, particularly during the
              period in which this report is being prepared;

         b)   Evaluated the effectiveness of the registrant's disclosure
              controls and procedures and presented in this report our
              conclusions about the effectiveness of the disclosure controls and
              procedures, as of the end of the period covered by this report
              based on such evaluation; and

         c)   Disclosed in this report any change in the registrant's internal
              control over financial reporting that occurred during the
              registrant's most recent fiscal quarter (the registrant's fourth
              fiscal quarter in the case of an annual report) that has
              materially affected, or is reasonably likely to materially affect,
              the registrant's internal control over financial reporting; and

   5.   The registrant's other certifying officer and I have disclosed, based on
        our most recent evaluation of internal control over financial reporting,
        to the registrant's auditors and the audit committee of the registrant's
        board of directors (or persons performing the equivalent functions):

         a)   All significant deficiencies and material weaknesses in the design
              or operation of internal control over financial reporting which
              are reasonably likely to adversely affect the registrant's ability
              to record, process, summarize and report financial information;
              and

         b)   Any fraud, whether or not material, that involves management or
              other employees who have a significant role in the registrant's
              internal control over financial reporting.

Date: March 12, 2004                       /s/  GREGORY E. A. MORRISON
                                           ----------------------------------
                                           Gregory E. A. Morrison
                                           President and Chief Executive Officer