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Accurate canceling of physiological tremor is extremely important in robotics-assisted surgical instruments/procedures. The performance of robotics-based hand-held surgical devices degrades in real time due to the presence of phase delay in sensors (hardware) and filtering (software) processes. Effective tremor compensation requires zero-phase lag in filtering process so that the filtered tremor signal can be used to regenerate an opposing motion in real time. Delay as small as 20 ms degrades the performance of human-machine interference. To overcome this phase delay, we employ multistep prediction in this paper. Combined with the existing tremor estimation methods, the procedure improves the overall accuracy by 60% for tremor estimation compared to single-step prediction methods in the presence of phase delay. Experimental results with developed methods for 1-DOF tremor estimation highlight the improvement.