The aim of this research is to develop analytical techniques that are supported by experimental data to predict the behavior of a passive magnetic damper in a cryogenic environment. The applications are far reaching--projects with high precision pointing requirements, such as JWST, operate in harsh environments where traditional damping techniques may be limited or ineffective. Therefore, we are interested in developing new technologies that can be used passively to isolate vibration disturbances effectively at a temperature of 40 K, under conditions that offer only a few nanometers of relative motion. Magnetic damping relies on the principle of motional EMF. As a conductor passes through a magnetic field, eddy currents form to produce a force that opposes the direction of motion. The magnitude of this force depends on several factors including the characteristics of the conductor and the magnetic field, which may be highly dependent on temperature. Current research is focused on material characterization, and a simple test cell has been designed to evaluate the damping, quantify the temperature effects, and expand our predictive capabilities. Several material combinations have been successfully cycled from 295K to 15 K, and the results, which illustrate damping from 1% to 100% critical damping, will be presented and compared to model predictions.