The quarantine of identified close contacts has been vital to reducing transmission rates and averting secondary infection risk before symptom onset and by asymptomatic cases. The effectiveness of this contact tracing strategy to mitigate transmission is sensitive to the adherence to quarantines, which may be lower for longer quarantine periods or in vaccinated populations (where perceptions of risk are reduced). This study develops a simulation model to evaluate contact tracing strategies based on the sequential testing of identified contacts after exposure as an alternative to quarantines, in which contacts are isolated only after confirmation by a positive test. The analysis considers different number and types of tests (PCR and lateral flow antigen tests (LFA)) to identify the cost-effective testing policies that minimize the expected infecting days post-exposure considering different levels of testing capacity. This analysis suggests that even a limited number of tests can be effective at reducing secondary infection risk: two LFA tests (with optimal timing) avert infectiousness at a level that is comparable to 14-day quarantine with 90% adherence; adding a third test (PCR or LFA) reaches the efficiency of a 95% quarantine adherence. These results are robust to the exposure dates of the contact, which suggests that simple testing rules can be effective for improving contact tracing in settings where strict quarantine adherence is difficult to implement.