Abstract Background The COVID-19 pandemic has resulted in the closure or partial closure of international borders in almost all countries. Here, we investigate the efficacy of imported case detection considering quarantine length and different testing measures for travellers on arrival. Methods We examine eight broad border control strategies from utilizing quarantine alone, pre-testing, entry and exit testing, and testing during quarantine. In comparing the efficacy of these strategies, we calculate the probability of detecting travellers who have been infected up to 2 weeks pre-departure according to their estimated incubation and infectious period. We estimate the number of undetected infected travellers permitted entry for these strategies across a prevalence range of 0.1–2% per million travellers. Results At 14-day quarantine, on average 2.2% (range: 0.5–8.2%) of imported infections are missed across the strategies, leading to 22 (5–82) imported cases at 0.1% prevalence per million travellers, increasing up to 430 (106–1641) at 2%. The strategy utilizing exit testing results in 3.9% (3.1–4.9%) of imported cases being missed at 7-day quarantine, down to 0.4% (0.3–0.7%) at 21-day quarantine, and the introduction of daily testing, as the most risk averse strategy, reduces the proportion further to 2.5–4.2% at day 7 and 0.1–0.2% at day 21 dependent on the tests used. Rapid antigen testing every 3 days in quarantine leads to 3% being missed at 7 days and 0.7% at 14 days, which is comparable to PCR testing with a 24-hour turnaround. Conclusions Mandatory testing, at a minimal of pre-testing and on arrival, is strongly recommended where the length of quarantining should then be determined by the destination country’s level of risk averseness, pandemic preparedness and origin of travellers. Repeated testing during quarantining should also be utilized to mitigate case importation risk and reduce the quarantining duration required.