This paper presents a set of analytical expressions used to determine the coupling coefficient between primary and secondary Litz-wire planar coils used in a transcutaneous energy transfer (TET) system. A TET system has been designed to power a novel elastic scaling artificial anal sphincter system (ES-AASS) for treating severe fecal incontinence (FI), a condition that would benefit from an optimized TET. Expressions that describe the geometrical dimension dependence of self- and mutual inductances of planar coils on a ferrite substrate are provided. The effects of ferrite substrate conductivity, relative permeability, and geometrical dimensions are also considered. To verify these expressions, mutual coupling between planar coils is computed by 3D finite element analysis (FEA), and the proposed expressions show good agreement with numerical results. Different types of planar coils are fabricated with or without ferrite substrate. Measured results for each of the cases are compared with theoretical predictions and FEA solutions. The theoretical results and FEA results are in good agreement with the experimental data.