Self consistent solution to electromagnetic (EM)-circuit systems is of significant interest for a number of applications. This has resulted in exhaustive research on means to couple them. In time domain, this typically involves a tight integration (or coupling) with field and non-linear circuit solvers. This is in stark contrast to coupled analysis of linear/weakly non-linear circuits and EM systems in frequency domain. Here, one typically extracts equivalent port parameters that are then fed into the circuit solver. Such an approach has several advantages; (a) the number of ports is typically smaller than the number of degrees of freedom, resulting in cost savings; (b) is circuit agnostic; (c) can be integrated with a variety of device models. Port extraction is tantamount to obtaining impulse response of the linear EM system. In time domain, the deconvolution required to effect this is unstable. Recently, a novel approach was developed for time domain integral equations to overcome this bottleneck. We extend this approach to time domain finite element method, and demonstrate its utility via a number of examples; significantly, we demonstrate that self consistent solutions obtained using either a fully coupled or port extraction is identical to the desired precision for non-linear circuit systems. This is shown within a nodal network. We also demonstrate integration of port extracted data directly with drift diffusion equation to model device physics.