Insulation failure is a significant driver of failures in electromagnetic coils, which are used, for example, in motor and solenoid applications. A promising method of assessing the health of insulation in electromagnetic coils is the use of broadband terminal impedance measurements. Previous research has focused on the resonant frequency of the coil impedance response as a feature to reflect insulation health. This paper performs a sensitivity analysis of an equivalent circuit model for the electromagnetic coil in order to survey the frequency spectrum for frequencies that can be applied in insulation health monitoring. The results show that while resonant frequency is sensitive to changes in the insulation, there are frequencies around the resonant frequency that are many times more sensitive to these changes, and hence should be preferred for insulation health monitoring purposes. With this knowledge, health monitoring system designers can understand where in the frequency spectrum insulation health data can best be located, allowing for an effective health monitoring system design.