Hand-held robotic instruments are developed to compensate physiological tremor in real-time while augmenting the required precision and dexterity into normal microsurgical work-flow. 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 (3D) tip position control involves modeling and canceling the tremor in 3-axes (x, y, and z axes) separately. Our analysis with the tremor data recorded from surgeons and novice subjects show that there exists significant correlation in tremor motion across the dimensions. Motivated by this, a new multi-dimensional modeling approach based on extreme learning machines (ELM) is proposed in this paper to correct the phase delay and to accurately model tremulous motion in three dimensions simultaneously. A study is conducted with tremor data recorded from the microsurgeons to analyze the suitability of proposed approach.