The scientific and engineering communities are relying more and more on numerical models to simulate ever-increasingly complex phenomena. Selecting a model, from among a family of models that meets the simulation requirements, presents a challenge to modern-day analysts. To address this concern, a framework is adopted anchored in info-gap decision theory. The framework proposes to select models by examining the trade-offs between prediction accuracy and sensitivity to epistemic uncertainty. The framework is demonstrated on two structural engineering applications by asking the following question: Which model, of several numerical models, approximates the behavior of a structure when parameters that define each of those models are unknown? One observation is that models that are nominally more accurate are not necessarily more robust, and their accuracy can deteriorate greatly depending upon the assumptions made. It is posited that, as reliance on numerical models increases, establishing robustness will become as important as demonstrating accuracy.