Social matching systems recommend people to people. In an ideal world, such systems could be context-aware, in that they would introduce users to each other in situations where they are mutually interested, available and open to meeting (i.e., facilitate a valuable encounter). Unfortunately, today's systems primarily match individuals based on simple similarity and proximity metrics. This paper explores how contextual information available on today's mobile phones could be used to identify opportunities for people to make valuable new connections. Three types of context that are relevant for this work are: relational, social and personal. We present insights gained from several iterations of semi-structured interviewing (N=58) exploring these three types of contexts and propose novel context-aware social matching concepts such as: Sociability of others as an indicator of opportune social context; activity involvement as an indicator of opportune personal context; and contextual rarity as an indicator of opportune relational context.