The nearby elliptical galaxies NGC 4621 and NGC 4697 each host a supermassive black hole with M• > 108 M☉. Analysis of archival Chandra data and new NRAO Very Large Array data shows that each galaxy contains a low-luminosity active galactic nucleus (LLAGN), identified as a faint, hard X-ray source that is astrometrically coincident with a faint 8.5-GHz source. The latter has a diameter less that 0.3'' (26 pc for NGC 4621, 17 pc for NGC 4697). The black holes energizing these LLAGNs have Eddington ratios L(2–10 keV)/L(Edd) ~ 10−9, placing them in the so-called quiescent regime. The emission from these quiescent black holes is radio-loud, with log RX = log ν Lν(8.5 GHz)/L(2–10 keV) ~ − 2, suggesting the presence of a radio outflow. Also, application of the radio-X-ray-mass relation from Yuan & Cui for quiescent black holes predicts the observed radio luminosities ν Lν(8.5 GHz) to within a factor of a few. Significantly, that relation invokes X-ray emission from the outflow rather than from an accretion flow. The faint, but detectable, emission from these two massive black holes is therefore consistent with being outflow-dominated. Observational tests of this finding are suggested.