The proper understanding and modeling of a microcalorimeter's response requires accurate knowledge of a handful of parameters, such as C, G, α. While a few of these parameters are directly determined from the IV characteristics, some others, notoriously the heat capacity (C) and α, appear in degenerate combinations in most measurable quantities. The consideration of a complex microcalorimeter leads to an added ambiguity in the determination of the parameters. In general, the dependence of the microcalorimeter's complex impedance on these various parameters varies with frequency. This dependence allows us to determine individual parameters by fitting the prediction of the microcalorimeter model to impedance data. In this paper we describe efforts at characterizing the Goddard X-ray microcalorimeters. With the parameters determined by this method, we compare the pulse shape and noise spectra predictions to data taken with the same devices.