Human connection is essential for our personal well-being and a building block for a well-functioning society. There is a prominent interest in the potential of technology for mediating social connection, with a wealth of systems designed to foster the feeling of connection between strangers, friends, and family. By surveying this design landscape we present a transitional definition of mediated genuine connection and nine design strategies embodied within 50 design artifacts: affective self-disclosure, reflection on unity, shared embodied experience, transcendent emotions, embodied metaphors, interpersonal distance, touch, provocations, and play. In addition to drawing on design practice-based knowledge we also identify underlying psychological theories that can inform these strategies. We discuss design considerations pertaining to sensory modalities, vulnerability-comfort trade-offs, consent, situatedness in context, supporting diverse relationships, reciprocity, attention directedness, pursuing generalized knowledge, and questions of ethics. We hope to inspire and enrich designers' understanding of the possibilities of technology to better support a mediated genuine feeling of connection.