Increasingly, there is a recognized need for secure information sharing. In order to implement information sharing between diverse organizations, we need privacypreserving interoperation systems. In this work, we describe two frameworks for privacy-preserving interoperation systems. Ontology matching is an indispensable component of interoperation systems. To implement privacy-preserving interoperation systems, we need privacy-preserving ontology matching algorithms. In this paper, we outline frameworks for privacy-preserving ontology matching and discuss the privacy implications of the frameworks.