Despite the appeal of screening travelers during emerging infectious disease outbreaks, evidence shows that syndromic and questionnaire-based programs are largely ineffective in preventing or delaying the geographic spread of infection. Molecular tests offer high sensitivity and specificity, and can detect infections earlier than symptom screening, suggesting potential for improved outcomes, yet molecular tests were used to screen travelers for COVID-19 with mixed success. To investigate why screening for COVID-19 was not more successful, and to quantify the limits of screening for other pathogens of concern, we developed a probabilistic model that incorporates within-host viral kinetics. We then evaluated the potential effectiveness of screening travelers with molecular tests for influenza A, SARS-CoV-1, SARS-CoV-2, and Ebola virus. Even under highly optimistic assumptions about behavior and test characteristics, we find screening effectiveness is always limited because the infections with the highest transmission potential are undetectable at the time of travel, an idea we term the fundamental limit of traveler screening. We also demonstrate how estimates of ascertainment are a misleading substitute for screening effectiveness because they overestimate reductions in transmission at the destination. Understanding these limitations can guide the deployment of future traveler screening programs and inform strategies to improve outbreak prevention and control.