Imperfect detection methods make it difficult to tell whether an invasive species has been successfully eradicated. However, management cannot continue indefinitely when individuals are no longer detected – at some point, efforts must be reduced or ceased entirely. The risks of mistakenly inferring that an eradication attempt has been successful can be high: the species can bounce back and even expand its range, causing environmental and economic damage, and rendering the initial eradication campaign redundant. This decision problem, balancing the risks of declaring eradication prematurely with the costs of continued management, is currently being contemplated by managers of the fox eradication programme on Phillip Island, in Victoria, Australia. We used a Bayesian catch-effort model to analyse data on the number of foxes removed and sighted using different methods. We estimate that there were 11 foxes remaining on Phillip Island as of end of June 2012. Baiting was the most effective method for removing foxes per person-hour invested, and spotlighting was the most effective method for sighting foxes without removal. We then projected forward into the future, assuming management effort continues at current levels, but no further foxes are detected (removed or sighted). Under this scenario, the mean estimate for the number of foxes remaining drops below a single fox after three years with no detections, and the probability that eradication has been successful is 0.69. This is the optimal time to declare eradication, given our estimated cost of declaring eradication prematurely. This framework indicates the minimum number of years for which management of foxes on the island must continue and allows decision makers to assess the trade-offs involved in any decision to declare eradication.