Invasive species are a well-recognized cause of environmental and economic damage. Restricting the costs of invaders is difficult, however, because the vectors that introduce invaders also introduce many species that bring benefits to society. Thus, a challenge for ecologists is to produce risk assessment tools for determining the identity and location of future invaders so that their establishment can be prevented. Recent work towards these goals has produced a number of tools with high accuracy, but their economic utility has been questioned because false positives inevitably lead to valuable species being excluded from trade and to locations not at risk being protected. We have constructed two ecologically realistic models to test the conditions under which risk assessments add economic value to prevention efforts. The first of these tests how accurate a risk assessment needs to be to provide economic benefits when used to determine which species should be allowed for import. When applied to the Australian trade in ornamental plants, this model showed that risk assessments with accuracies greater than ~70% produce net economic benefits. Our second model tests the economic utility of applying predictions of invader spread in prevention efforts. We have applied this model to the rusty crayfish invasion of Vilas County, Wisconsin, and show that data available in the mid-1970s were sufficient to construct a model that, if used to guide prevention, would have produced net economic benefits of ~$5million over the last 30 years. In combination, these models demonstrate that ecological predictions have a large role to play for informing the management of invasion pathways.