Improving solar cell efficiency is an enormously powerful driver of the cost reduction of solar power. While the silicon solar cell efficiency approaches theoretical limits, many thin-film solar cell technologies fall behind. In particular, cadmium telluride (CdTe) solar cells have only reached a maximum efficiency of 22.1%. One of the challenges associated with the development of CdTe solar cells is due its high electron affinity and the difficulty of achieving heavy p-type doping. This challenge results in the formation of a Schottky barrier at the hole contact, which reduces solar cell efficiency, primarily through the reduction of open circuit voltage (Voc) and fill factor (FF). The Schottky barrier makes the characterization of the actual solar cell p-n junction through current voltage (I-V), capacitance voltage (C-V), and thermal admittance spectroscopy (TAS) more difficult and not straightforward. However, interpreted through accurate physical models and under the correct experimental conditions, these techniques can then also be used to extract the impact of the contact on device performance, chiefly through analysis of the barrier height. Additionally, characterization of the open circuit voltage as a function of the illumination intensity (Suns-Voc) and the open circuit voltage as a function of temperature [Voc(T)] offer insight into the potential impact of the contact barrier. A comprehensive review of characterization of the barrier through the above techniques is given, primarily through a two-diode model. Further, a discussion of the utility of electrochemical capacitance-voltage (ECV) profiling to recover carrier concentrations in device regions otherwise difficult to access through traditional C-V measurements is provided along with modeling to support this conclusion. A discussion of and justification for the experimental extraction of barrier height from TAS measurements are also provided. Experimentally measured Voc(T), C-V, and Suns-Voc characteristics are presented and compared for a CdTe and a gallium arsenide (GaAs) solar cell. Experimental results indicate that the contact barriers and other possible non-idealities strongly affect the performance of the CdTe solar cell. Modeling results demonstrate the use of ECV to characterize solar cell absorbers can offer information unavailable via conventional C-V measurements.