Traveller screening is being used to limit further global spread of 2019 novel coronavirus (nCoV) following its recent emergence. Here, we project the impact of different travel screening programs given remaining uncertainty around the values of key nCoV life history and epidemiological parameters. Even under best-case assumptions, we estimate that screening will miss more than half of infected travellers. Breaking down the factors leading to screening successes and failures, we find that most cases missed by screening are fundamentally undetectable, because they have not yet developed symptoms and are unaware they were exposed. These findings emphasize the need for measures to track travellers who become ill after being missed by a travel screening program. We make our model available for interactive use so stakeholders can explore scenarios of interest using the most up-to-date information. We hope these findings contribute to evidence-based policy to combat the spread of nCoV, and to prospective planning to mitigate future emerging pathogens.