In this paper, we present a combined experimental and computational study of the thermomechanical reliability of multilayer ceramic capacitors (MLCC's). We focus on residual stresses introduced into the components during the cooling down step of the sintering process. The technique of microindentation turned out to be a useful method to measure the stresses locally. The computations were done with three-dimensional finite element simulations. We find that the cooling step introduces compressive in-plane stresses in the ceramic layers. There is reasonably good overall agreement between the residual stresses obtained from the indentation experiments and the numerical simulations. Some discrepancies do exist, though, for measurements on cross-sectioned MLCC's. Possible reasons for the differences are discussed.