AIMS: We aimed to determine the effectiveness of surveillance using testing for SARS-CoV-2 to identify an outbreak arising from a single case of border control failure in a country that has eliminated community transmission of COVID-19: New Zealand. METHODS: A stochastic version of the SEIR model CovidSIM v1.1 designed specifically for COVID-19 was utilised. It was seeded with New Zealand population data and relevant parameters sourced from the New Zealand and international literature. RESULTS: For what we regard as the most plausible scenario with an effective reproduction number of 2.0, the results suggest that 95% of outbreaks from a single imported case would be detected in the period up to day 36 after introduction. At the time point of detection, there would be a median number of five infected cases in the community (95% range: 1-29). To achieve this level of detection, an ongoing programme of 5,580 tests per day (1,120 tests per million people per day) for the New Zealand population would be required. The vast majority of this testing (96%) would be of symptomatic cases in primary care settings and the rest in hospitals. CONCLUSIONS: This model-based analysis suggests that a surveillance system with a very high level of routine testing is probably required to detect an emerging or re-emerging SARS-CoV-2 outbreak within five weeks of a border control failure in a nation that had previously eliminated COVID-19. Nevertheless, there are plausible strategies to enhance testing yield and cost-effectiveness and potential supplementary surveillance systems such as the testing of town/city sewerage systems for the pandemic virus.