Materials for extreme electrical contacts need to have high electrical conductivity coupled with good structural properties. Potential applications include motor contacts, high power switches, and the components of electromagnetic launch (EML) systems. In particular, the lack of durability of these materials in rail components limits practical EML implementation. These rails experience significant amounts of Joule heating, due to extreme current densities, and subsequent thermally-assisted wear. New more durable materials solutions are needed for these components. A systematic materials selection study was executed to identify and compare candidate materials solutions. Several possible candidate non-dominated materials as well as hybrid materials that could potential fill the "white spaces" on the Ashby charts were identified. A couple potential candidate materials were obtained and evaluated. These included copper-tungsten W-Cu, "self-lubricating" graphite-impregnated Cu, and Gr-W-Cu composites with different volume fractions of the constituents. The structure-property relations were determined through mechanical and electrical resistivity testing. A unique test protocol for exposing mechanical test specimens to extreme current densities up to 1.2 GA/m2 was developed and used to evaluate these candidate materials. The systematic design of multi-functional materials for these extreme electrical contacts requires more than an empirical approach. Without a good understanding of both the tribological and structural performance, the optimization of the microstructure will not be quickly realized. By using micromechanics modeling and other materials design modeling tools coupled with systematic mechanical and tribological experiments, the design of materials for these applications can potentially be accelerated. In addition, using these tools, more complex functionally-graded materials tailored to the application can be systematically designed. In this study, physics- and micromechanics-based models were used to correlate properties to the volume fraction of the constituents of the evaluated candidate materials. Properties correlated included density, elastic modulus, hardness, strength, and electrical resistivity of the W-Cu materials.