  We present a re-calibration of the $M_{BH}-\sigma_{\star}$ relation, based on
a sample of 16 reverberation-mapped galaxies with newly determined bulge
stellar velocity dispersions ($\sigma_{\star}$) from integral-field
spectroscopy (IFS), and a sample of 32 quiescent galaxies with publicly
available IFS. For both samples, $\sigma_{\star}$ is determined via two
different methods that are popular in the literature, and we provide fits for
each sample based on both sets of $\sigma_{\star}$. We find the fit to the AGN
sample is shallower than the fit to the quiescent galaxy sample, and that the
slopes for each sample are in agreement with previous investigations. However,
the intercepts to the quiescent galaxy relations are notably higher than those
found in previous studies, due to the systematically lower $\sigma_{\star}$
measurements that we obtain from IFS. We find that this may be driven, in part,
by poorly constrained measurements of bulge effective radius ($r_{e}$) for the
quiescent galaxy sample, which may bias the $\sigma_{\star}$ measurements low.
We use these quiescent galaxy parameterizations, as well as one from the
literature, to recalculate the virial scaling factor $f$. We assess the
potential biases in each measurement, and suggest $f=4.82\pm1.67$ as the best
currently available estimate. However, we caution that the details of how
$\sigma_{\star}$ is measured can significantly affect $f$, and there is still
much room for improvement.
