Square arrays of gold~(\ce{Au}) hemispheroids deposited on a UV-transparent glass substrate reveal a rich optical response when investigated by spectroscopic Mueller Matrix Ellipsometery. Two samples were studied; the first consisted of hemispheroids of parallel and perpendicular radii of \SI{54}{\nano\meter} and \SI{25}{\nano\meter} (relative to the surface of the substrate) and the lattice constant was \SI{210}{\nano\meter}; the corresponding parameters for the second sample were \SI{28}{\nano\meter}, \SI{18}{\nano\meter} and \SI{125}{\nano\meter}, respectively. By a full azimuthal rotation of the samples, we observe all the Rayleigh anomalies corresponding to grazing diffracted waves, with strong resonances for co-polarization scattered light near the high symmetry points and cross-polarization scattered light around the Localized Surface Plasmon Resonance~(LSPR). Polarization-conversion becomes particularly important at grazing incidence, and the cross-polarization follows the Rayleigh lines. In this paper we focus on the classical problem of modelling the approximately uniaxial (``block diagonal'') ellipsometric response of these \ce{Au} metallic particles on substrates supporting a LSPR. The results of the Bedeaux-Vlieger~(BV) formalism are compared to similar results obtained by a full-wave numerical simulations based on the Finite Element Method and with direct inversion for the effective (substrate dependent) dielectric function. It is found that for a regular 2D lattice, the BV formalism can extract reasonable parameters related to particle dimensions, as long as the Rayleigh anomalies are well above the LSPR. However, the weak polarization conversion around the LSPR and the small dispersion of the LSPR with respect to the azimuthal rotation of the substrate cannot be modelled within the BV formalism. The finite element method used in COMSOL is evaluated as one of many numerical tools to analyze ellipsometric spectra. Finally, we refine a method to calculate the uniaxial effective dielectric function from the excess susceptibilities of the BV model.