Travel restrictions, while delaying the spread of an emerging disease from the source, could inflict substantial socioeconomic burden. Travel-related policies, such as quarantine and testing of travelers, may be considered as alternative strategies to mitigate the negative impact of travel bans. We developed a meta-population, delay-differential model to evaluate a strategy that combines testing of travelers prior to departure from the source of infection with quarantine and testing at exit from quarantine in the destination population. Our results, based on early parameter estimates of SARS-CoV-2 infection, indicate that testing travelers at exit from quarantine is more effective in delaying case importation than testing them before departure or upon arrival. We show that a 1-day quarantine with an exit test could outperform a longer, 3-day quarantine without testing in delaying the outbreak peak. Rapid, large-scale testing capacities with short turnaround times provide important means of detecting infectious cases and reducing case importation, while shortening quarantine duration for travelers at destination.