The operating conditions of scramjet engines demand designs that include active cooling by the fuel and the use of lightweight materials that withstand extreme heat fluxes under oxidizing conditions. The goal of this analysis is to provide an optimization tool that can be used to direct the development of advanced materials that outperform existing high temperature alloys and compete with ceramic matrix composites. For this purpose an actively cooled plate has been optimized for minimum weight under three primary constraints. (i) Resistance to pressure loads arising from fuel injection and combustion, as well as thermal loads associated with the combustion temperature. (ii) A temperature distribution in the structure during operation that does not exceed material limits, subject to a reasonable pressure drop. (iii) A maximum temperature in the fuel (JP-7) low enough to prohibit coking. It is shown that all design requirements typical of Mach 5-7 hypersonic vehicles can be met by a small subset of material systems. Those made using C/SiC composites are the lightest. Others made using Nb alloys and (thermal barrier coated) superalloys are somewhat heavier, but might prevail in a design selection because of their structural robustness, facility of fabrication and cost-effectiveness.