A two-stage supercritical (SC) desalination system is proposed to treat highly saline brines to high-purity steam that could be used in power generation. Highly saline brines with up to similar to 20% salt content are pressurized and heated to SC conditions of 500 degrees C and 3500 psi to rapidly precipitate the dissolved salts and generate SC steam containing similar to 100 ppm salts. Two highly saline brines, collected from an oil field and a deep saline formation, and two concentrated NaCl solutions were treated in the SC desalination system. A SC membrane separation system with carbon filters is developed and used to purify the SC steam to a high purity level. Promising carbon filters or membranes prepared and tested for purifying SC steam included a porous graphite disk, a flexible graphite sheet, and a carbon nanotube-based membrane. The best performing membranes exhibited a very high water flux of similar to 200-800 kg/m(2).h, with a salt rejection of >90%.