This paper addresses the subject of local error estimators for finite element methods involving local enrichment. More precisely, we focus on the extended finite element method, which was developed in the last decade for fracture mechanics. We present a method for the calculation of accurate strict bounds of mixed-mode stress intensity factors associated with an extraction operator and the theory of error in constitutive relation. This method has already been shown to be effective for standard finite elements. The objective of this paper is to show that it can easily be adapted to the extended finite element method.