The delays between exposure and reporting present obvious challenges for monitoring the success of control measures using reported case-count data. We suggest that two different kinds of monitoring will be important if distancing measures are to be relaxed: (1) monitoring cases through testing, contact tracing, and other case finding, and (2) monitoring contact patterns and distancing behaviour in the population, in a “distancing surveillance” effort. This latter form of monitoring, derived from mobile phones, surveys and apps, could be available rapidly, whereas the incubation period places an unavoidable delay between control measures and detecting their impact in reported cases—even if testing of symptomatic cases were widespread and reporting were immediate. There is considerable interest in real-time monitoring of mobile phone movements, population surveys on the uptake of physical distancing, and other behavioural data. While these are potentially promising avenues, the outcome of interest is incident infections. Locations of mobile phones, traffic patterns, and survey information are proxies for this outcome at best. The work we have presented here could help to calibrate distancing surveillance measurements, to understand how they relate to changes in contact rates for modelling efforts.