Exhibit 4(b)

                           CERTIFICATION PURSUANT TO
                 SECTION 302 OF THE SARBANES OXLEY ACT OF 2002



I, Ian Webber, certify that:

1.   I have reviewed this annual report on Form 40-F/A of CP Ships Limited;

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 issuer as of, and for, the periods presented in this report;

4.   The issuer'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 issuer
     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
          issuer, 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 issuer'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 issuer's internal control
          over financial reporting that occurred during the period covered by
          the annual report that has materially affected, or is reasonably
          likely to materially affect, the issuer's internal control over
          financial reporting; and

5.   The issuer's other certifying officer and I have disclosed, based on our
     most recent evaluation of internal control over financial reporting, to
     the issuer's auditors and the audit committee of the issuer'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 issuer'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 issuer's internal
          control over financial reporting.

Date:  12 November 2004


                                      By:     /s/ Ian Webber
                                              ------------------------
                                      Name:   Ian Webber
                                      Title:  Chief Financial Officer