Exhibit 23.1 CONSENT OF INDEPENDENT PUBLIC ACCOUNTANTS As independent public accountants, we hereby consent to the incorporation by reference of our report dated February 19, 1999, included in this Form 10-K, into Callon Petroleum Company's previously filed Registration Statements on Forms S-8 (File Nos. 33-90410, 333-29537 and 333-29529). Arthur Andersen LLP New Orleans, Louisiana March 29, 1999