  (ABRIDGED) We present stellar velocity dispersion (sigma*) measurements for a
significant sample of 40 broad-line (Type 1) active galaxies for use in testing
the well-known relation between black hole mass and stellar velocity
dispersion. The objects are selected to contain Ca II triplet, Mgb triplet, and
Ca H+K stellar absorption features in their optical spectra so that we may use
them to perform extensive tests of the systematic biases introduced by both
template mismatch and contamination from the active galactic nucleus (AGN). We
use the Ca II triplet as a benchmark to evaluate the utility of the other
spectral regions in the presence of AGN contamination. Broad Fe II emission,
extending from ~5050-5520 A, in combination with narrow coronal emission lines,
can seriously bias sigma* measurements from the Mgb region, highlighting the
need for extreme caution in its use. However, we argue that at luminosities
constituting a moderate fraction of the Eddington limit, when the Fe II lines
are both weak and smooth relative to the stellar lines, it is possible to
derive meaningful measurements with careful selection of the fitting region. In
particular, to avoid the contamination of coronal lines, we advocate the use of
the region 5250--5820 A, which is rich in Fe absorption features. We lay the
groundwork for an extensive comparison between black hole mass and bulge
velocity dispersion in active galaxies, as described in a companion paper by
Greene & Ho.
