It is widely recognized that screening is an imperfect barrier to spread (Bitar et al., 2009; Cowling et al., 2010; Gostic et al., 2015; Mabey et al., 2014; Quilty et al., 2020), due to: the absence of detectable symptoms during the incubation period; variation in the severity and detectability of symptoms once the disease begins to progress; imperfect performance of screening equipment or personnel; or active evasion of screening by travellers. Previously we estimated the effectiveness of traveller screening for a range of pathogens that have emerged in the past, and found that arrival screening would miss 50–75% of infected cases even under optimistic assumptions (Gostic et al., 2015). Yet the quantitative performance of different policies matters for planning interventions and will influence how public health authorities prioritize different measures as the international and domestic context changes. Here we use a mathematical model to analyse the expected performance of different screening measures for COVID-19, based on what is currently known about its natural history and epidemiology and on different possible combinations of departure and arrival screening policies.