Time-reversal methods are widely used to achieve wave focusing in acoustics and electromagnetics. Past time-reversal experiments typically require that a transmitter be initially present at the target focusing point, which limits the application of this technique. In this paper, we propose a method to focus waves at an arbitrary location inside a complex enclosure using a numerically calculated wave excitation signal. We use a semiclassical ray algorithm to calculate the signal that would be received at a transceiver port resulting from the injection of a short pulse at the desired target location. The time-reversed version of this signal is then injected into the transceiver port, and an approximate reconstruction of the short pulse is created at the target. The quality of the pulse reconstruction is quantified in three different ways, and the values of these metrics are shown to be predicted by the statistics of the scattering parameter |S_{21}|^{2} between the transceiver and target points in the enclosure over the bandwidth of the pulse. We demonstrate the method experimentally using a flat microwave billiard, and we quantify the reconstruction quality as a function of enclosure loss, port coupling, and other considerations.