In legged robot state estimation without foot-contact measurements, nominal gait phase does not directly indicate the instantaneous validity of foot–ground kinematic constraints, while residual errors in state propagation and kinematic pseudo-measurements can further bias the state estimate. A contact-reliability-aware neural residual Kalman filtering framework is developed while retaining the physics-based state-space model and Kalman recursion. A multi-task temporal estimator infers gait-phase-constrained continuous contact reliability together with dynamic and observation residuals from proprioceptive history sequences. The estimated reliability regulates contact-related process and measurement covariances to adjust the confidence assigned to foot–ground kinematic constraints. The dynamic residual compensates base-velocity prediction errors, and the observation residual corrects predictable errors in foot kinematic pseudo-measurements through the measurement innovation. Simulation results show lower base-state and foot-position errors than the Binary Contact Kalman filter across multiple motion commands. Physical walking and turning experiments show improved horizontal base trajectory estimation and lower terminal drift within the prescribed onboard update period.