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                                                                    EXHIBIT 31.1

             CERTIFICATION OF CHIEF EXECUTIVE OFFICER, PURSUANT TO

                  SECTION 302 OF THE SARBANES-OXLEY ACT OF 2002


     I, Timothy O'Malley, certify that:

     1.   I have reviewed this report on Form 10-Q for Medwave, Inc. (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 and results of operations and cash
          flows of the Registrant as of, and for, the periods presented in this
          report;

     4.   I am 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 my
               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.   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:   February 4, 2005


                                              By:  /s/ Timothy J. O'Malley
                                                   ----------------------------
                                                   Timothy J. O'Malley
                                                   President and Chief Executive
                                                   Officer (Principal Executive
                                                   Officer and Principal
                                                   Financial Officer)