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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 Annual Report on Form 10-K for the fiscal year
ended December 31, 2004 (this "Report") 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)) and internal control over financial
reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) 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)    Designed such internal control over financial reporting, or caused
            such internal control over financial reporting to be designed under
            our supervision to provide reasonable assurance regarding the
            reliability of financial reporting and the preparation of financial
            statements for external purposes in accordance with generally
            accepted accounting principles;

      c)    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

      d)    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

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      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 15, 2005                       /s/  GREGORY E. A. MORRISON
                                           -------------------------------------
                                           Gregory E. A. Morrison
                                           President and Chief Executive Officer

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