We propose a framework for estimation and inference when the model may be misspecified. We rely on a local asymptotic approach where the degree of misspecification is indexed by the sample size. We construct estimators whose mean squared error is minimax in a neighborhood of the reference model, based on simple one-step adjustments. In addition, we provide confidence intervals that contain the true parameter under local misspecification. To interpret the degree of misspecification, we map it to the local power of a specification test of the reference model. Our approach allows for systematic sensitivity analysis when the parameter of interest may be partially or irregularly identified. As illustrations, we study two binary choice models: a cross-sectional model where the error distribution is misspecified, and a dynamic panel data model where the number of time periods is small and the distribution of individual effects is misspecified.