Ontology reuse saves costs and improves interoperability. Knowing which ontology to reuse is difficult without proper quality assessment. We provide a framework that enables quality assessment in the form of user reviews of ontologies, which are ranked based on inter-user trust. Open Rating Systems allow to collect user reviews, ratings, and information on trust between users, and to exploit this information for computing a personalized ranking of ontologies. In the traditional Open Rating System model, objects can only be rated as a whole, and other users can only be trusted globally. Since these limitations hinder the use of an Open Rating System for applications like ontology rating, we develop an extension, our Topic-Specific Trust Open Rating System. Our system features topic-specific trust and multi-faceted ratings. In a simulation, we show that our Topic-Specific Open Rating System provides a better result than the Open Rating System. In a user study, we show that having user ratings and result ranking based on our system significantly facilitates ontology selection for the end user, compared to the state of the art ontology search engines.