Our goal is to investigate protein networks conserved between different organisms. Given the protein interaction networks for two species and a list of homologous pairs of protein in the two species, we propose a model for measuring whether two subnetworks, one in each protein interaction network, are conserved. Our model separately measures the degree of conservation of the two subnetworks and the quality of the edges in each subnetwork. We propose an algorithm for finding pairs of networks, one in each protein interaction network, with high conservation and high quality. When applied to publicly-available protein-protein interaction data and gene sequences for baker's yeast and fruit fly, our algorithm finds many conserved networks with a high degree of functional enrichment. Using our method, we find many conserved protein interaction networks involved in functions such as DNA replication, protein folding, response to heat, protein serine/threonine phosphatase activity, kinase activity, and ATPase activity.