Rendezvous is a fundamental building block in distributed cognitive radio networks (CRNs), where users must find a jointly available channel. Research on the rendezvous problem has focused so far on minimizing the time to rendezvous (to find a suitable channel) or on maximizing the degree (number of channels on which rendezvous can take place). In this paper, we model the rendezvous problem in a more realistic way that acknowledges the fact available channels may suffer from interference, and interference may vary among users in different locations over time. In this setting, CRNs benefit from rendezvous methods that find a quiet channel, which supports high symbol rates and does not suffer much from dropped packets. We propose algorithms that achieve this goal for both initial rendezvous problem (users share no prior information) and continuous rendezvous problem (users who have already established a link must vacate the channel and seek another). We propose both deterministic and randomized methods based on mapping the channel set to a larger set in a way that gives preference to quiet channels. This technique allows us to add interference-awareness to existing rendezvous algorithms. We analyze the new algorithms and substantiate our analyses through extensive simulations.