Developing high quality systems depends on developing high quality models. An important facet of model quality is their consistency with respect to their meta-model. We call the verification of this quality the conformance checking process. We are interested in the conformance checking of Product Line Models (PLMs). The problem in the context of product lines is that product models are not created by instantiating a meta-model: they are derived from PLMs. Therefore it is usually at the level of PLMs that conformance checking is applied. On the semantic level, a PLM is defined as the collection of all the product models that can be derived from it. Therefore checking the conformance of the PLM is equivalent to checking the conformance of all the product models. However, we would like to avoid this naïve approach because it is not scalable due to the high number of models. In fact, it is even sometimes infeasible to calculate the number of product models of a PLM. Despite the importance of PLM conformance checking, very few research works have been published and tools do not adequately support it. In this paper, we present an approach that employs Constraint Logic Programming as a technology on which to build a PLM conformance checking solution. The paper demonstrates the approach with feature models, the de facto standard for modeling software product lines. Based on an extensive literature review and an empirical study, we identified a set of 9 conformance checking rules and implemented them on the GNU Prolog constraints solver. We evaluated our approach by applying our rules to 50 feature models of sizes up to 10000 features. The evaluation showed that our approach is effective and scalable to industry size models.