Abstract We study contact tracing in a new macro-epidemiological model with asymptomatic transmission and limited testing capacity. Contact tracing is a testing strategy that aims to reconstruct the infection chain of newly symptomatic agents. This strategy may be unsuccessful because of an externality leading agents to expand their interactions at rates exceeding policymakers’ ability to test all the traced contacts. Complementing contact tracing with timely deployed containment measures (e.g., social distancing or a tighter quarantine policy) corrects this externality and delivers outcomes that are remarkably similar to the benchmark case where tests are unlimited. We provide theoretical underpinnings to the risk of becoming infected in macro-epidemiological models. Our methodology to reconstruct infection chains is not affected by curse-of-dimensionality problems.