Modern autopilot systems are prone to sensor attacks that can jeopardize flight safety. To mitigate this risk, we proposed a modular solution: the secure safety filter, which extends the well-established control barrier function (CBF)-based safety filter to account for, and mitigate, sensor attacks. This module consists of a secure state reconstructor (which generates plausible states) and a safety filter (which computes the safe control input that is closest to the nominal one). Differing from existing work focusing on linear, noise-free systems, the proposed secure safety filter handles bounded measurement noise and, by leveraging reduced-order model techniques, is applicable to the nonlinear dynamics of drones. Software-in-the-loop simulations and drone hardware experiments demonstrate the effectiveness of the secure safety filter in rendering the system safe in the presence of sensor attacks.