Transfer functions are useful parameters for ultrawideband (UWB) antenna characterization. The response of an antenna system to any excitation can be completely determined in terms of the transfer functions (or the "impulse response" in time domain) of the antennas. In this paper, the transfer functions are defined as a transmitting antenna transfer function, a receiving antenna transfer function, and an antenna system transfer function to characterize UWB antenna systems readily and accurately. The transfer functions are expressed by ABCD and S parameters when the antenna system is considered as a two-port network. As examples, an antipodal Vivaldi antenna and a disc cone antenna are investigated to validate the proposed method. The measured results are further verified by XFDTD simulation.