The use of superconductors for power transmission has been studied for decades. The lossless nature of superconducting cables makes the system less stable operationally because damping normally provided by resistive losses is eliminated. Breaker actions during routine system operations or in response to faults can trigger high frequency oscillations between the inductances and capacitances from either power factor correction capacitors or parasitic phase-to-phase or phase-to-ground capacitances in the lines or cables. Transient overvoltages may exceed double the nominal operating voltage. In a power system using conventional conductors, series resistance damps these oscillations within a number of 60 Hz cycles. In a superconducting system, these oscillations persist, with only the light damping from the frequency-dependent resistance of the superconductors, creating a long-lasting distortion on voltage and current. Traditional methods to damp transient oscillations may not be effective for every situation. Power electronic converters may damp these oscillations. Either a shunt- or a series-connected power converter is an option. However, a series connected converter must carry the full line current at all times, but a shunt-connected converter damps oscillations only when they occur. Key issues are rating the power converter and reducing energy losses.