Physiological hand tremor impedes microsurgery. We present both a novel adaptive algorithm for tremor estimation and a new technique for active real-time cancelling of physiological tremor. Tremor is modeled online using the weighted-frequency Fourier linear combiner (WFLC). This adaptive algorithm models tremor as a modulating sinusoid, and tracks its frequency, amplitude and phase. Piezoelectric actuators move the surgical instrument tip in opposition to the motion of tremor, effectively subtracting the tremor from the total motion. We demonstrate the technique in 1D using a cantilever apparatus as a benchtop simulation of the surgical instrument. Actual hand motion, prerecorded during simulated surgery, is used as input. In 25 tests, WFLC tremor compensation reduces the RMS tip motion in the 6-16 Hz tremor band by 67%, and reduces the RMS error with respect to an a posteriori estimate of voluntary motion by 30%. The technique can be implemented in a hand-held microsurgical instrument.