We describe the design of an eddy current brake for use as programmable viscous damper for haptic interfaces. Unlike other types of programmable brakes, eddy current brakes can provide linear, programmable physical damping that can be modulated at high frequency. These properties makes them well suited as dissipative actuators for haptic interfaces. We overview the governing physical relationships, and describe design optimization for inertial constraints. A prototype haptic interface is described, and experimental results are shown that illustrate the improvement in stability when simulating a stiff wall that is made possible using programmable eddy current dampers.