Conversational search (CS) has recently become a significant focus of the information retrieval (IR) research community. Multiple studies have been conducted which explore the concept of conversational search. Understanding and advancing research in CS requires careful and detailed evaluation. Existing CS studies have been limited to evaluation based on simple user feedback on task completion. We propose a CS evaluation framework which includes multiple dimensions: search experience, knowledge gain, software usability, cognitive load and user experience, based on studies of conversational systems and IR. We introduce these evaluation criteria and propose their use in a framework for the evaluation of CS systems.