This paper describes ongoing efforts to design large surface area cooling modules suitable for sustained operation at heat fluxes approaching 50 MW/m2. Modules having actively cooled areas of 10 cm2 or more are being developed. Cooling is provided by an array of small diameter water jets operating at speeds of 40 to 50 m/s. These jets impinge on the rear side of a metallic faceplate 2 to 3 mm thick from which the heat load is absorbed. Thermal stress in the faceplate is the expected causes of module failure at high flux, owing to stress levels that may exceed yield strength. We describe our design and the performance estimates for these cooling modules. The behavior of cooling jet arrays is summarized, including numerical simulations for our specific case. Analytical and finite element studies of the stresses in candidate faceplate materials are described for typical thermal and mechanical conditions. The effect of faceplate mounting is a particular issue. A design for a thin-film high-flux resistance heater is also discussed; this heater provides the heat load for testing module prototypes. These cooling modules are intended to be useful in a broad range of applications.