  High-accuracy black hole (BH) masses require excellent spatial resolution
that is only achievable for galaxies within ~100 Mpc using present-day
technology. At larger distances, BH masses are often estimated with
single-epoch scaling relations for active galactic nuclei. This method requires
only luminosity and the velocity dispersion of the broad line region (BLR) to
calculate a virial product, and an additional virial factor, $f$, to determine
BH mass. The accuracy of these single-epoch masses, however, is unknown, and
there are few empirical constraints on the variance of $f$ between objects. We
attempt to calibrate single-epoch BH masses using spectropolarimetric
measurements of nine megamaser galaxies from which we measure the velocity
distribution of the BLR. We do not find strong evidence for a correlation
between the virial products used for single-epoch masses and dynamical mass,
neither for the megamaser sample alone or when combined with dynamical masses
from reverberation mapping modeling. Furthermore, we find evidence that the
virial parameter $f$ varies between objects, but we do not find strong evidence
for a correlation with other observable parameters such as luminosity or broad
line width. Although we cannot definitively rule out the existence of any
correlation between dynamical mass and virial product, we find tension between
allowed $f$ values for masers and those widely used in the literature. We
conclude that the single-epoch method requires further investigation if it is
to be used successfully to infer BH masses.
