Electro-optic waveguide modulators exploiting the carrier-induced epsilon-near-zero effect in transparent conducting oxides are comprehensively studied and evaluated using a rigorous multi-physics modeling framework. The examined amplitude modulators integrate indium tin oxide with two representative examples of the silicon-on-insulator technology, the silicon-rib and silicon-slot platform, with the latter design exhibiting superior performance, featuring μm modulation lengths, switching speeds exceeding 100 GHz, and a sub-pJ per bit of energy consumption. The effect of free carriers is rigorously introduced by combining the drift-diffusion model for the description of the carrier dynamics with near-infrared carrier-dependent permittivity models, leading to a seamless and physically consistent integration of solid-state physics and Maxwell wave theory on a unified finite-element platform.