The value of serological testing to inform the public health response to the SARS-CoV-2 pandemic is debated. Using a transmission model, we examined how serology can be implemented to allow seropositive individuals to resume more normal levels of social interaction while offsetting the risks. We simulated the use of widespread serological testing with realistic assay characteristics, in which seropositive individuals partially restore their social contacts and act as immunological shields. If social distancing is relaxed by 50% at the same time that quarterly serological screening is initiated, approximately 120,000 deaths could be averted and a quarter of the US population could be released from social distancing in the first year of the epidemic, compared to a scenario without serological testing. This strategy has the potential to substantially flatten the COVID-19 epidemic curve while also allowing a substantial number of individuals to safely return to social and economic interactions.