  We present relations of the black hole mass and the optical luminosity with
the velocity dispersion and the luminosity of the [Ne V] and the [O IV]
high-ionization lines in the mid-infrared (MIR) for 28 reverberation-mapped
active galactic nuclei. We used high-resolution Spitzer Infrared Spectrograph
and Infrared Space Observatory Short Wavelength Spectrometer data to fit the
profiles of these MIR emission lines that originate from the narrow-line region
of the nucleus. We find that the lines are often resolved and that the velocity
dispersion of [Ne V] and [O IV] follows a relation similar to that between the
black hole mass and the bulge stellar velocity dispersion found for local
galaxies. The luminosity of the [Ne V] and the [O IV] lines in these sources is
correlated with that of the optical 5100A continuum and with the black hole
mass. Our results provide a means to derive black hole properties in various
types of active galactic nuclei, including highly obscured systems.
