A system for measuring nanometer motions of microscopic structures is demonstrated. Stop-action images of a target are obtained with a light microscope, CCD camera, and stroboscopic illuminator. Motions are determined directly from measured images using algorithms from computer vision. The accuracy of motion measurements using the system is assessed using a moving target with calibrated displacements. Accuracy is determined for specimens viewed under our most optimal conditions as well as for a number of suboptimal conditions that illustrate important degradation mechanisms. Measured errors are compared to predictions based on computer simulations of theoretical models. Results show that the most important hardware factors include substrate vibrations and camera imperfections. Measurement errors for the most optimal hardware conditions are primarily due to systematic bias in the computer vision algorithms. For our most optimal conditions, the system can resolve motions as small as nanometers. Thus, errors in motion measurements are small compared to both the wavelength of the light used to obtain the images and the pixel spacing of the video microscope.