An illumination system that has an output luminance (brightness) LO that is greater than the intrinsic output luminance (brightness) LI of the light emitting diodes used within the system. The system utilizes one or more light emitting diodes having highly reflective surfaces and recycles a portion of the light generated by the light emitting diodes back to the light emitting diodes in order to enhance the effective luminance. The illumination system includes a light-reflecting cavity and one or more highly reflective light emitting diodes having total surface area AS mounted inside the cavity, either on the interior surfaces of the cavity or within the cavity volume. The cavity has a light output aperture of area AO. The light emitting diodes have reflectivity RS. The exposed inside surfaces of the light-reflecting cavity have reflectivity RC. In order to achieve enhanced brightness, it is required that the area of the light output aperture AO be less than the total area AS of the light emitting diodes. It is preferred that reflectivity RC and reflectivity RS each be at least 50%, more preferably 75% and most preferably 90%. Illumination systems with enhanced luminance resulting from light recycling may be used in projection displays, flat-panel displays, avionics displays, automotive lighting, residential lighting, commercial lighting and industrial lighting applications.