Mobile social matching systems have the potential to transform the way we make new social ties, but only if we are able to overcome the many challenges that exist as to how systems can utilize contextual data to recommend interesting and relevant people to users and facilitate valuable encounters between strangers. This article outlines how context and mobility influence people's motivations to meet new people and presents innovative design concepts for mediating mobile encounters through context-aware social matching systems. Findings from two studies are presented. The first, a survey study (n = 117) explored the concept of contextual rarity of shared user attributes as a measure to improve desirability in mobile social matches. The second, an interview study (n = 58) explored people's motivations to meet others in various contexts. From these studies we derived a set of novel context-aware social matching concepts, including contextual sociability and familiarity as an indicator of opportune social context; contextual engagement as an indicator of opportune personal context; and contextual rarity, oddity, and activity partnering as an indicator of opportune relational context. The findings of these studies establish the importance of different contextual factors and frame the design space of context-aware social matching systems.