In this work, a three-dimensional microstructure-scale model of a Solid Oxide Fuel Cell’s Positive-Electrolyte-Negative assembly is applied for the purpose of investigating the impact of decreasing the electrolyte thickness on the magnitude, and the composition of electrochemical losses generated within the cell. Focused-Ion-Beam Scanning Electron Microscopy reconstructions are used to construct a computational domain, in which charge transport equations are solved. Butler–Volmer model is used to compute local reaction rates, and empirical relationships are used to obtain local conductivities. The results point towards three-dimensional nature of transport phenomena in thin electrolytes, and electrode-electrolyte interfaces.