Electrochemical impedance spectroscopy is a widely used tool to study electrochemical reactions in batteries, fuel cells and other electrochemical energy conversion devices. However, conduction processes in the electrolyte of high temperature fuel or electrolysis cells (SOFC/SOEC) are inaccessible during operation, severely restricting the information that can be obtained about performance and degradation of the electrolyte. Using the distribution function of relaxation times (DRT), we study the ionic conduction properties and degradation phenomena in multi-layered solid electrolytes, ex situ and at low temperatures. The investigation of full cells in air enables a detailed analysis of the conductivity of supported electrolytes as thin as 1 mu m, as well as the relative contributions of multilayered electrolytes. Furthermore, three case studies are presented concerning the degradation mechanism in SOFC and SOEC operation, showcasing the ability of this technique to distinguish the effects of grain boundary contamination, formation of solid solutions and the formation of porosity on the ionic conductivity of thin, supported electrolytes.