Ceramic materials are an attractive choice in many applications due to their excellent high temperature properties, light weight, and corrosion resistance. Due to the high cost of manufacturing and fabrication of ceramics, conventional metallic materials are an integral part of most typical ceramic based engineering applications. Consequently, to take advantage of both material strengths, there must be a joint between the ceramic and metal components. The high thermal expansion mismatch between ceramic and metal components and temperature dependent material properties of each component make the joining problem a complex one. In this ceramic-to-metal joint study, finite element analysis was used to identify significant parameters controlling stresses arising from thermal expansion. The simulation is, however, restricted to a brazed joint between silicon nitride and 4140 annealed steel, which has an extremely high thermal expansion mismatch. In order to reduce the effects of this thermal expansion mismatch, a number of real and fictitious materials have been studied for their potential as compliance layers. This systematic simulation of ceramic-to-metal joints has provided insight to the effects of Young's modulus (YM), thermal expansion coefficient (TEC), thickness of individual layers, and their specific arrangement between the ceramic and steel components. It was shown by simulation that a crack in the ceramic to metal joint changes the stress distribution drastically. Consequently, it is indispensable to include the simulation of cracks in a ceramic-to-metal joint in order to avoid erroneous conclusions. A simple one dimensional design formula was developed for the ceramic-to-metal joint. This formula can be used to screen/select materials for compliance layers and help in reducing the number of materials to be tested to finalize the choice of compliance layers.