Starshades provide a leading technology to enable the direct detection and spectroscopic characterization of Earth-like exoplanets. Two key aspects to advancing starshade technology are the demonstration of starlight suppression at science-enabling levels and validation of optical models at this high level of suppression. These technologies are addressed in current efforts underway at the Princeton Starshade Testbed. Recent experimental data suggest we are observing the effects of vector (non-scalar) diffraction, which are limiting the starshade's performance and preventing the scalar optical models from agreeing with experimental results at the deepest levels of suppression. This report outlines a model developed to simulate vector diffraction in the testbed using a full solution to Maxwell's equations propagating through narrow features of the starshade. We find that experimental results can be explained by vector diffraction as light traverses the thickness of the starshade mask and that our model is in rough agreement with observations. We provide simulation results of a number of starshade geometries as a first attempt to understand the relation of these effects to properties of the starshade masks. Finally, we outline a number of possible solutions aimed to minimize vector effects and to allow us to reach our milestone of 10-9 suppression.