High-efficiency crystalline silicon (c-Si) solar cells increasingly feature sophisticated electron and hole contacts aimed at minimizing electronic losses. At the rear of photovoltaic devices, such contacts - usually consisting of stacks of functional layers - offer opportunities to enhance the infrared response of the solar cells. Here, we propose an accurate and simple modeling procedure to evaluate the infrared performance of rear contacts in c-Si solar cells. Our method combines full-wave electromagnetic modeling of the rear contact with a statistical ray optics model to obtain the fraction of optical energy dissipated from the rear contact relative to that absorbed by the Si wafer. Using this technique, we study the impact of the refractive index, extinction coefficient, and thickness of the rear-passivating layer and establish basic design rules. In addition, we evaluate novel optical structures, including stratified thin films, nanoparticle composites, and conductive nanowires embedded in a low-index dielectric matrix, for integration into advanced rear contacts in c-Si photovoltaic devices. From an optical perspective, nanowire structures preserving low contact resistance appear to be the most effective approach to mitigating dissipation losses from the rear contact.