Harmful and often catastrophic damages from the introduction of non-indigenous species (NIS) are widely acknowledged. While preventing the introduction of NIS through border and pre-border measures has been the first line of defence, post-border surveillance has recently attracted considerable attention as it increases the likelihood that small invasive populations will be found and eradicated quickly before they become widespread. We develop a novel and practical optimal surveillance model across space and a number of surveillance techniques for four different invasive pests, determining where and how to best allocate resources to detect and eradicate these pests. Our focus is on Barrow Island, a Class A Nature Reserve in Australia, home to thousands of native plants and animals, many endemic to the island, where limited industrial activity and environmental protection coexist. It is also home to the world's largest non-government quarantine and surveillance system. Our results provide a unique platform that finds the maximum net benefit from post-border surveillance expenditures across species, locations, and surveillance methods, thus protecting a key environmental asset.