Modern software systems are deployed in a highly dynamic, uncertain environment. Ideally, a system that is \emph{robust} should be capable of establishing its most critical requirements even in the presence of possible \emph{deviations} in the environment. We propose a technique called \emph{behavioral robustification}, which involves systematically and rigorously improving the robustness of a design against potential deviations. Given behavioral models of a system and its environment, along with a set of user-specified deviations, our robustification method produces a redesign that is capable of satisfying a desired property even when the environment exhibits those deviations. In particular, we describe how the robustification problem can be formulated as a \emph{multi-objective optimization} problem, where the goal is to restrict the deviating environment from causing a violation of a desired property, while maximizing the amount of existing functionality and minimizing the cost of changes to the original design. We demonstrate the effectiveness of our approach on case studies involving the robustness of an electronic voting machine and safety-critical interfaces.