Ensuring safety for dynamic systems in the presence of state estimation errors is challenging because safety guarantees must hold for the unknown true state while only an uncertain estimate is available. Control Barrier Function (CBF) based safety filters can become overly conservative under state estimation uncertainty, leading to deadlocks in narrow passages even when a safe path exists. We present Confidence-Adaptive Lipschitz-Managed Control Barrier Functions (CALM–CBFs) to reduce this conservatism, guaranteeing safety while improving the robot’s overall performance. CALM–CBF adapts the safety margin to both local estimation confidence and how sensitive the safety constraint is in the current part of the state space, rather than using a single worst-case margin everywhere. A risk-aware supervisor then trades off allowed speed against conservatism, relaxing the margin when progress stalls near tight gaps and restoring stricter behavior when clearance improves. In simulation, our method reduces the conservatism up to 68.5% compared to a measurement-robust CBF baseline, while still avoiding collisions and resolving deadlocks in narrow passages.