The performance of surgical robotic devices in real-time mainly depends on phase-delay in sensors and filtering process. A phase delay of 16-20 ms is unavoidable in these robotics procedures due to the presence of hardware low pass filter in sensors and pre-filtering required in later stages of cancellation. To overcome this phase delay, we employ multi-step prediction with band limited multiple Fourier linear combiner (BMFLC) and Autoregressive (AR) methods. Results show that the overall accuracy is improved by 60% for tremor estimation compared to single-step prediction methods in the presence of phase delay. Experimental results with the proposed methods for 1-DOF tremor estimation highlight the improvement.