In the elderly, there have been reports of above 10% of the population being diagnosed with pathological tremor. Some patients find the conventional medical solutions, which primarily include medications and surgery, insufficient to treat their conditions. Technologies to mechanically suppress tremor have been proposed as a potential alternative. Robotic solutions for suppressing human tremor typically revolve around identifying and isolating the tremor motion component. This study proposes instead to only estimate the intentional movement and reject any disturbance that interferes with such an intended movement. By designing the control feedback such that motions other than the voluntary are rejected, the tremor component is attenuated. The controller components include an outer-loop admittance feedback loop and an internal velocity feedback loop. Additionally, a state feedback is utilized to improve the velocity tracking. To test the proposed approach, a benchtop tremor simulation device (TSD) was developed. The TSD consists of two motors, which, respectively, simulate the motion of a human joint and the suppressing action of a mechanical suppression system. A parametric stability analysis of the proposed tremor-suppression strategy is presented. A motion profile recorded from a person with tremor is used as human input in the TSD to experimentally validate the proposed tremor rejection strategy. Spectral analysis results show a 99.8% tremor reduction; the power reduction related to the voluntary movement is instead negligible (0.18%). Tracking of a velocity profile results in a small root-mean-square (rms) error (0.58 rad/s). The paper concludes by comparing the proposed approach to others presented in the literature.