During outbreaks of high-consequence pathogens, airport screening programs have been deployed to curtail geographic spread of infection. The effectiveness of screening depends on several factors, including pathogen natural history and epidemiology, human behavior, and characteristics of the source epidemic. We developed a mathematical model to understand how these factors combine to influence screening outcomes. We analyzed screening programs for six emerging pathogens in the early and late stages of an epidemic. We show that the effectiveness of different screening tools depends strongly on pathogen natural history and epidemiological features, as well as human factors in implementation and compliance. For pathogens with longer incubation periods, exposure risk detection dominates in growing epidemics, while fever becomes a better target in stable or declining epidemics. For pathogens with short incubation, fever screening drives detection in any epidemic stage. However, even in the most optimistic scenario arrival screening will miss the majority of cases.