Many safety failures in machine learning arise when models are used to assign predictions to people (often in settings like lending, hiring, or content moderation) without accounting for how individuals can change their inputs. In this work, we introduce a formal validation procedure for the responsiveness of predictions with respect to interventions on their features. Our procedure frames responsiveness as a type of sensitivity analysis in which practitioners control a set of changes by specifying constraints over interventions and distributions over downstream effects. We describe how to estimate responsiveness for the predictions of any model and any dataset using only black-box access, and how to use these estimates to support tasks such as falsification and failure probability estimation. We develop algorithms that construct these estimates by generating a uniform sample of reachable points, and demonstrate how they can promote safety in real-world applications such as recidivism prediction, organ transplant prioritization, and content moderation.