A numerical method for determining the broadband characteristic impedance of an antenna is described. The method is based on a solution of the electric field integral equation for the antenna surface subject to a strongly localized incident field, representative of a desired transient source voltage. A method is outlined for calculating, from the numerically simulated feed current, the frequency-dependent impedance spectrum of a finite antenna, subject to a sharp pulse. It is shown that this may be used to determine reliably the characteristic impedance of TEM antennas. Particular attention is paid to the problem of effectively modeling the feed region of the transient antenna. A general approach which ensures the stability and accuracy (to within a few percent) of solutions is described. It uses surface patches to model the antenna and obviates potential difficulties associated with thin wire models of the feed region.