Precision, robustness, dexterity, and intelligence are the design indices for current generation surgical robotics. To augment the required precision and dexterity into normal microsurgical work-flow, handheld robotic instruments are developed to compensate physiological tremor in real time. The hardware (sensors and actuators) and software (causal linear filters) employed for tremor identification and filtering introduces time-varying unknown phase delay that adversely affects the device performance. The current techniques that focus on three-dimensions (3-D) tip position control involves modeling and canceling the tremor in three axes (x-, y-, and z -axes) separately. Our analysis with the tremor recorded from surgeons and novice subjects shows that there exists significant correlation in tremor across the dimensions. Based on this, a new multidimensional modeling approach based on extreme learning machines is proposed in this paper to correct the phase delay and to accurately model 3-D tremor simultaneously. Proposed method is evaluated through both simulations and experiments. Comparison with the state-of-the art techniques highlight the suitability and better performance of the proposed approach for tremor compensation in handheld surgical robotics.