We present new radio and X-ray observations of two nearby (<4 Mpc) low-mass early-type galaxies with dynamically confirmed central black holes: NGC 5102 and NGC 205. NGC 5102 shows a weak nuclear X-ray source and has no core radio emission. However, for the first time we demonstrate that it shows luminous extended radio continuum emission in low-resolution, low-frequency (<3 GHz) data, consistent with jet lobes on scales ≳100 pc formed from past accretion and jet activity. By contrast, in new, extremely deep, strictly simultaneous Very Large Array and Chandra observations, no radio or X-ray emission is detected from the black hole in NGC 205. We consider these measurements and upper limits in the context of the few other low-mass early-type galaxies with dynamically confirmed black holes, and show that the mean ratio of bolometric to Eddington luminosity in this sample is only
log
(
L
bol
/
L
Edd
)
=
−
6.57
±
0.50
. These Eddington ratios are lower than typical in a comparison sample of more massive early-type galaxies, though this conclusion is quite tentative due to our small sample of low-mass galaxies and potential biases in the comparison sample. This preliminary result is in mild tension with previous work using less sensitive observations of more distant galaxies, which predict higher X-ray luminosities than we observe for low-mass galaxies. If it is confirmed that central black holes in low-mass galaxies typically have low Eddington ratios, this presents a challenge to measuring the occupation fraction of central black holes with standard optical emission line, X-ray, or radio surveys.