Rehabilitation robots may be used to accurately measure the mechanical impedance of the human arm in order to quantitatively assess the motor function of a patient undergoing neurorehabilitation therapy. However, the high cost of these robotic systems and their required sensors has posed a barrier to widespread clinical use. We present a technique to measure the mechanical impedance of the human arm without the need for a physical force sensor to measure human-robot interaction forces. Instead, these forces are accurately estimated by a virtual sensor that incorporates the robot's kinematics and dynamics, along with acceleration measurements from an inexpensive accelerometer. The identification techniques are validated on a mass-spring system of known impedance and are subsequently applied to data collected from the human arm.