As conversational agents like Siri and Alexa gain in popularity and use, conversation is becoming a more and more important mode of interaction for search. Conversational search shares some features with traditional search, but differs in some important respects: conversational search systems are less likely to return ranked lists of results (a SERP), more likely to involve iterated interactions, and more likely to feature longer, well-formed user queries in the form of natural language questions. Because of these differences, traditional methods for search evaluation (such as the Cranfield paradigm) do not translate easily to conversational search. In this work, we propose a framework for offline evaluation of conversational search, which includes a methodology for creating test collections with relevance judgments, an evaluation measure based on a user interaction model, and an approach to collecting user interaction data to train the model. The framework is based on the idea of “subtopics”, often used to model novelty and diversity in search and recommendation, and the user model is similar to the geometric browsing model introduced by RBP and used in ERR. As far as we know, this is the first work to combine these ideas into a comprehensive framework for offline evaluation of conversational search.