While models of terahertz frequency plasmons in two-dimensional electron systems are usually developed by reducing the number of spatial dimensions, fully three-dimensional models may be needed for the design and analysis of realistic structures. Using full-wave electromagnetic simulations, we have analysed the plasmons and magnetoplasmons observed in two recent experiments. Here, we demonstrate agreement between the theoretical and the experimental results, and discuss further device characteristics such as plasmon transmission, reflection, absorption, and field distributions. We then compare the three-dimensional full-wave simulations with a two-dimensional model. Finally, we discuss approaches for increasing signal transmission and reducing reflection, with direct relevance for improving future experiments.