Recent work at the National Institute of Standards and Technology (NIST) with superconducting transition thermometers suggests that substantial improvements could be achieved in the detection capability of electrical-substitution radiometers, which are widely used as the most accurate absolute standards of radiant flux and irradiance. Cambridge Research & Instrumentation (CRI) has constructed liquid-nitrogen and liquid-helium-cooled prototype radiometers with responsivities of 550 mK/mW and 3.5 K/mW, and natural time constants of 30 s and 3 s, respectively. Our results with the liquid-nitrogen-cooled radiometer show that the high-T_c superconductor YBCO sensor has similar detection capability to a germanium resistance thermometer operating at 4 K. In this prototype radiometer, we were able to control receiver temperature to better than 1 µK and to attain a root-mean-square (rms) noise level of 1.6 nW. Our ongoing work focuses on the absolute accuracy achievable with such a liquid-nitrogen-cooled radiometer, using an optimized thermal design. The high detection sensitivity offered by the Nb sensor in the liquid-helium-cooled prototype radiometer achieved a temperature stability of 40 nK (rms), which implies a noise-equivalent power of 10 pW. Our measurements indicate that 1 pW should be feasible with optimized electronics, a lower-T_c sensor, and better control of heat-sink and scene drifts through implementation in the NIST Low Background Infrared (LBIR) chamber.