The extended finite element method (XFEM) is now one of many successful numerical methods to solve fracture mechanics problems. The particular advantage of the XFEM, which relies on the partition of unity property of finite element (FE) shape functions, is its ability to model cracks without the mesh conforming to their geometry. This chapter presents different approaches to control the discretization error committed by enriched FE approximations, decrease human intervention in damage tolerance assessment of complex industrial structures, and enhance confidence in the results by providing enriched finite element methods with sound error estimators which will guarantee a predetermined accuracy level and suppress recourse to manual iterations and heuristics. Error estimators can normally overestimate or underestimate the exact error. For this reason, the use of bounding techniques that guarantee certain levels of accuracy is preferred.