This paper discusses the conceptual design of a shuttle-attached Liquid Droplet Radiator (LDR) experiment. The Liquid Droplet Radiator is an advanced lightweight heat rejection concept that can be used to reject heat from future high-powered space platforms. In the LDR concept, submillimeter-sized droplets are generated, radiate heat as they pass through space and are then collected and recirculated back to the heat source. The LDR experiment is designed to be attached to the shuttle longeron and integrated into the shuttle bay using standard shuttle/experiment interfaces. Overall power, weight, and data requirements of the experiment are detailed. Conceptual design and shuttle integration issues are discussed.