In this article a route to analyze the full optical response of plasmonic structures is developed. First, the simple case of an anisotropic thin plasmonic layer supported on a transparent substrate is analyzed by introducing a quantity named anisotropic surface excess function (ASEF). The spectral features are analyzed in terms of effective dielectric function, demonstrating a more direct relation with the plasmonic response of the layer. The formalism is then generalized using a transfer matrix method. The formalism developed is supported by experimental evidence obtained by measuring the response of anisotropic nanoparticle arrays grown at a glancing angle. The agreement between theory and experiment is clear, suggesting that SE can be conveniently employed to measure the spectroscopic response of plasmonic structures. It is also demonstrated that the figure of merit of the plasmonic resonance for refractive index sensing can be greatly improved, with optimized measurement configurations, using polarized spectroscopy. ; Science Foundation of Ireland, (06/IN.1/I91) (11/RFP.1/PHY/3047); Higher Education Authority (PRTLI 4 - INSPIRE programme); Government of Rep. of Kazakhstan (The Bolashak programme)