Conceptual models such as database schemas, ontologies or process models have been established as a means for effective engineering of information systems. Yet, for complex systems, conceptual models are created by a variety of stakeholders, which calls for techniques to manage consistency among the different views on a system. Techniques for model matching generate correspondences between the elements of conceptual models, thereby supporting effective model creation, utilization, and evolution. Although various automatic matching tools have been developed for different types of conceptual models, their results are often incomplete or erroneous. Automatically generated correspondences, therefore, need to be reconciled, i.e., validated by a human expert. We analyze the reconciliation process in a network setting, where a large number of conceptual models need to be matched. Then, the network induced by the generated correspondences shall meet consistency expectations in terms of mutual reinforcing relations between the correspondences. We develop a probabilistic model to identify the most uncertain correspondences in order to guide the expert's validation work. We also show how to construct a set of high-quality correspondences, even if the expert does not validate all generated correspondences. We demonstrate the efficiency of our techniques for real-world datasets in the domains of schema matching and ontology alignment.