Air travel plays an important role in the cross-border spread of infectious diseases. During the SARS-CoV-2 pandemic many countries introduced strict border testing protocols to monitor the incursion of the virus. However, high implementation costs and significant inconvenience to passengers have led public health authorities to consider alternative methods of disease surveillance at borders. Aircraft wastewater monitoring has been proposed as one such alternative. In this paper we assess the theoretical limits of aircraft wastewater monitoring and compare its performance to post-arrival border screening approaches. Using an infectious disease model, we simulate an unmitigated SARS-CoV-2 epidemic originating in a seed country and spreading to the United Kingdom (UK) through daily flights. We use a probabilistic approach to estimate the time of first detection in the UK in aircraft wastewater and respiratory swab screening. Across a broad range of model parameters, our analysis indicates that the median time between the first incursion and detection in wastewater would be approximately 17 days (IQR: 7–28 days), resulting in a median of 25 cumulative cases (IQR: 6–84 cases) in the UK at the point of detection. Comparisons to respiratory swab screening suggest that aircraft wastewater monitoring is as effective as random screening of 20% of passengers at the border, using a test with 95% sensitivity. For testing regimes with sensitivity of 85% or less, the required coverage to outperform wastewater monitoring increases to 30%. Analysis of other model parameters suggests that wastewater monitoring is most effective when used on long-haul flights where probability of defecation is above 30%, and when the target pathogen has high faecal shedding rates and reasonable detectability in wastewater. These results demonstrate the potential use cases of aircraft wastewater monitoring and its utility in a wider system of public health surveillance.