Verification of autonomous systems offline is a time-intensive and expensive process that is prone to error. Runtime assurance ensures safe system operation online, in-the-loop. Enforcing safety requires a formal mathematical encoding of what safety is. We prescribe safe system behavior using Signal Temporal Logic (STL), an expressive language for specifying time-varying behavior beyond invariance conditions or obstacle avoidance. Given an STL specification and a control system, this thesis contributes algorithms to realize runtime assurance on a miniature autonomous blimp. A theoretical framework is developed where an STL specification is enforced in a receding horizon fashion. When deployed on hardware, it is apparent that formal handling of uncertainty is vital to closing the sim-to-real gap. Thus, an interval-valued extension of STL is developed to handle both state uncertainty and parametric uncertainty within an STL specification itself. Then, a terminal condition is derived to ensure that existence of a safe input at one time implies existence of safe inputs in the future. A change of approach from the uncertainty-free setting is also needed to handle model inaccuracies while preserving computational tractability. A safe dynamically feasible trajectory is produced instead of safe control inputs for hardware directly. After appropriately modifying the theory to handle bounded uncertainty, the runtime assurance algorithm is successfully deployed on a blimp, ensuring safety in-the-loop on real hardware.