**Exhibit 31.1****CERTIFICATION**I, James P. Bryce, certify that:1. I have reviewed this quarterly report on Form 10-Q of IPC Holdings, Ltd.;2. Based on my knowledge, this report does not contain any untrue statement of a material factor omit to state a material fact necessary to make the statements made, in light of thecircumstances under which such statements were made, not misleading with respect to the periodcovered by this report;3. Based on my knowledge, the financial statements, and other financial information included inthis report, fairly present in all material respects the financial condition, results of operationsand cash flows of the registrant as of, and for, the periods presented in this report;4. The registrant’s other certifying officer(s) and I are responsible for establishing andmaintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules13a-15(f) and 15d-15(f)) for the registrant and have:(a) Designed such disclosure controls and procedures, or caused such disclosure controls andprocedures to be designed under our supervision, to ensure that material information relating tothe registrant, including its consolidated subsidiaries, is made known to us by others within thoseentities, particularly during the period in which this report is being prepared;(b) Designed such internal control over financial reporting, or caused such internal control overfinancial reporting to be designed under our supervision, to provide reasonable assurance regardingthe reliability of financial reporting and the preparation of financial statements for externalpurposes in accordance with generally accepted accounting principles;(c) Evaluated the effectiveness of the registrant’s disclosure controls and procedures andpresented in this report our conclusions about the effectiveness of the disclosure controls andprocedures, 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 financialreporting that occurred during the registrant’s most recent fiscal quarter (the registrant’s fourthfiscal quarter in the case of an annual report) that has materially affected or is reasonablylikely to materially affect, the registrant’s internal control over financial reporting;5. The registrant’s other certifying officer(s) and I have disclosed, based on our most recentevaluation of internal control over financial reporting, to the registrant’s auditors and the auditcommittee of the registrant’s board of directors (or persons performing the equivalent function):(a) All significant deficiencies and material weaknesses in the design or operation of internalcontrol over financial reporting which are reasonably likely to adversely affect the registrant’sability to record, process, summarize and report financial information; and(b) Any fraud, whether or not material, that involves management or other employees who have asignificant role in the registrant’s internal control over financial reporting.Date: July 28, 2006       /s/ James P. Bryce     James P. Bryce    Chief Executive Officer  
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