Respiratory rate is an extremely important but poorly monitored vital sign for medical conditions. Current modalities for respiratory monitoring are suboptimal. This paper presents a proof of concept of a new algorithm using a contactless ultra-wideband (UWB) impulse radar-based sensor to detect respiratory rate in both a laboratory setting and in a two-subject case study in the Emergency Department. This novel approach has shown correlation with manual respiratory rate in the laboratory setting and shows promise in Emergency Department subjects. In order to improve respiratory rate monitoring, the UWB technology is also able to localize subject movement throughout the room. This technology has potential for utilization both in and out of the hospital environments to improve monitoring and to prevent morbidity and mortality from a variety of medical conditions associated with changes in respiratory rate.