Compensating for sensorimotor noise and for temporal delays has been identified as a major function of the nervous system. Although these aspects have often been described separately in the frameworks of optimal cue combination or motor prediction during movement planning, control-theoretic models suggest that these two operations are performed simultaneously, and mounting evidence supports that motor commands are based on sensory predictions rather than sensory states. In this letter, we study the benefit of state estimation for predictive sensorimotor control. More precisely, we combine explicit compensation for sensorimotor delays and optimal estimation derived in the context of Kalman filtering. We show, based on simulations of human-inspired eye and arm movements, that filtering sensory predictions improves the stability margin of the system against prediction errors due to low-dimensional predictions or to errors in the delay estimate. These simulations also highlight that prediction errors qualitatively account for a broad variety of movement disorders typically associated with cerebellar dysfunctions. We suggest that adaptive filtering in cerebellum, instead of often-assumed feedforward predictions, may achieve simple compensation for sensorimotor delays and support stable closed-loop control of movements.