Business artifacts have appeared as a new paradigm to capture the information required for the complete execution and reasoning of a business process. Likewise, conformance checking is gaining popularity as a crucial technique that enables evaluating whether recorded executions of a process match its corresponding model. In this paper, conformance checking techniques are incorporated into a general framework to specify business artifacts. By relying on the expressive power of an artifact-centric specification, BAUML, which combines UML state and activity diagrams (among others), the problem of conformance checking can be mapped into the Petri net formalism and its results be explained in terms of the original artifact-centric specification. In contrast to most existing approaches, ours incorporates data constraints into the Petri nets, thus achieving conformance results which are more precise. We have also implemented a plug-in, within the ProM framework, which is able to translate a BAUML into a Petri net to perform conformance checking. This shows the feasibility of our approach.