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Fully coupled transient analysis of electromagnetic (EM)-circuit systems is highly desirable for a number of applications. Over the last decade or so, there have been several papers that present effective solutions to this problem within the context of full-wave differential or integral equation solvers. The method typically espoused is as follows: discretize the underlying EM system, couple with the circuit subsystem self-consistently, and then solve the coupled system. Within this framework, nonlinearities are easily accounted for in the solution process. This is in direct contrast to frequency domain analysis, wherein one defines ports that couple the EM and circuit subsystems, i.e., the representation of the EM system using an effective impedance/admittance as seen at the circuit terminals. This approach permits: 1) solution only at the circuit level and 2) one can readily incorporate different circuits without having to solve the coupled system repeatedly. Achieving the same functionality in the time domain is a challenge. In this paper, we present a solution to this problem. We will prescribe the means to effectively represent the EM subsystem in terms of a transient admittance, thus facilitating a solution to the coupled system via a circuit-level solve. Several results are presented that serve to validate the proposed approach and demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]