Protecting against terrorist attacks requires making decisions in a world in which attack probabilities are largely unknown. The potential for very large losses encourages a conservative perspective, in particular toward decisions that are robust. But robustness, in the sense of assurance against extreme outcomes, ordinarily is not the only desideratum in uncertain environments. We adopt Yakov Ben-Haim’s (2001b) model of information gap decision making to investigate the problem of inspecting a number of similar targets when one of the targets may be attacked, but with unknown probability. We apply this to a problem of inspecting a sample of incoming shipping containers for a terrorist weapon. While it is always possible to lower the risk of a successful attack by inspecting more vessels, we show that robustness against the failure to guarantee a minimum level of expected utility might not be monotonic. Robustness modeling based on expected utility and incorporating inspection costs yields decision protocols that are a useful alternative to traditional risk analysis.