Gigahertz transverse electromagnetic (GTEM) transmission cells have been previously used to experimentally study exposure of biological cells to ultra-wideband (UWB), monopolar, electromagnetic pulses. Using finite-difference time-domain (FDTD) simulations we examine the time-dependent electric field waveforms and energy dose spatial distributions within a finite volume of biological cell culture medium during these experiments. The simulations show that when one or more flasks containing cell culture media are placed inside the GTEM cell, the uniform fields of the empty GTEM cell are significantly perturbed. The fields inside the cell culture medium, representing the fields to which the biological cells are exposed, are no longer monopolar and are spatially highly nonuniform. These effects result from a combination of refraction and distortion of the incident wave, combined with excitation of resonant eigenmodes within the cell culture medium volume. The simulations show that these distortions of the incident waveform may be mitigated by supporting the sample on a high permittivity pedestal and modifying the incident waveform to more closely approximate a Gaussian pulse. Under all simulated conditions, the estimated maximum temperature rises are completely negligible, ensuring that any experimentally observed unusual cell function or histopathology can be associated with nonthermal effects.