The ion conductivity of two series of porous ceramic diaphragms impregnated with caustic potash was investigated by electrochemical impedance spectroscopy. To understand the impact of the pore structure on ion conductivity, the three-dimensional (3-D) pore geometry of the diaphragms was characterized with synchrotron x-ray absorption tomography. Ion migration was calculated based on an extended pore structure model, which includes the electrolyte conductivity and geometric pore parameters, for example, tortuosity (τ) and constriction factor (β), but no fitting parameters. The calculated ion conductivities are in agreement with the data obtained from electrochemical measurements on the diaphragms. The geometric tortuosity was found to be nearly independent of porosity. Pore path constrictions diminish with increasing porosity. The lower constrictivity provides more pore space that can effectively be used for mass transport. Direct measurements from tomographs of tortuosity and constrictivity opens new possibilities to study pore structures and transport properties of porous materials.