The use of semiconductors as substrate in microwave devices is becoming more common in the design and implementation of low-cost integrated circuits. The presence of a lossy substrate and the loss-reduction techniques, through modification of the interconnect geometry, result in significant frequency dependence of the per-unit-length (p.u.l) parameters of the transmission line. In this paper, an approach is presented for time-domain simulation of transmission lines implemented on a Si substrate. We use a finite-element method to extract the p.u.l parameters (as functions of frequency) for a given interconnect which has been fabricated over a low-resistivity Si substrate. A time-domain recursive convolution technique, based on approximating the transmission line parameters using Vector Fitting algorithm, is used to analyze the interconnect. We present a method to integrate the proposed approach within a general-purpose circuit simulator. This allows the simulation of interconnects terminated with arbitrary linear/nonlinear networks. Some simulation results are presented to show the capabilities of this method.