A fundamental concern in progressing airborne wind energy (AWE) operations toward commercial success is guaranteeing that safety requirements placed on the systems are met. Due to the high-dimensional complexity of AWE systems, however, formal mathematical robustness guarantees become difficult to compute. We draw on research from Hamilton–Jacobi (HJ) reachability analysis to compute an avoidance control maneuver for the path-following controller that enforces safety constraints on the system while maintaining the guidance strategy. In addition, the subzero level set of the computed value function inherent in HJ reachability analysis indicates the backward reachable set, the set of states from which it is possible to safely drive the system into a target set within a given time without entering undesirable states. Furthermore, to integrate the avoidance controller with the path-following controller, we derive the necessary switching law such that the avoidance maneuver is only initiated when a tether rupture is potentially imminent. We illustrate our results via extensive simulation-based studies.