This article focuses on Electrodynamic Wireless Power Transfer (EWPT), a low-frequency alternative to inductive-based WPT systems. EWPT replaces the inductive receiver with an electromechanical one, with a resonant frequency much lower (usually between 1 and 200 Hz). This technology enables higher efficiency wireless power transmission through conductive media, with reduced risks for nearby living forms. This article proposes a modeling and analysis of the maximum transmitted power with EWPT systems, taking into account the various constraints arising due to the electrical, magnetic, and mechanical nature of the system. After modeling the various parts of EWPT systems, the analytical upper bound of the transmitted power was derived from the system equations. Technological constraints were incorporated into this model to derive a realistic power boundary. Finally, a methodology for optimizing and assessing the performance of EWPT systems was proposed based on the derived equations. These models and optimization methodologies should help scientists assess and optimize EWPT systems more effectively.