  We present new measurements for the nuclear stellar velocity dispersion
$\sigma_{\ast}$ within sub-arcsecond apertures for 28 nearby galaxies. Our data
consist of Space Telescope Imaging Spectrograph (STIS) long-slit spectra
obtained with the G750M grating centred on the H$\alpha$ spectral range. We fit
the spectra using a library of single stellar population models and Gaussian
emission lines, while constraining in most cases the stellar-population content
from an initial fit to G430L STIS spectra. We illustrate how these
$\sigma_{\ast}$ measurements can be useful for constraining the mass
$M_{\bullet}$ of supermassive black holes (SBHs) by concentrating on the cases
of the lenticular galaxies NGC4435 and NGC4459. These are characterized by
similar ground-based half-light radii stellar velocity dispersion $\sigma_{\rm
e}$ values but remarkably different $M_{\bullet}$ as obtained from modelling
their central ionised-gas kinematics, where NGC4435 appears to host a
significantly undermassive SBH compared to what is expected from the
$M_{\bullet}-\sigma_{\rm e}$ relation. For both galaxies, we build Jeans
axisymmetric dynamical models to match the ground-based stellar kinematics
obtained with SAURON integral-field spectrograph, including a SBH with
$M_{\bullet}$ value as predicted by the $M_{\bullet}-\sigma_{\rm e}$ relation
and using high-resolution HST images taken with the Advanced Camera for Surveys
to construct the stellar-mass model. By mimicking the HST observing conditions
we use such reference models to make a prediction for the nuclear
$\sigma_{\ast}$ value. Whereas this was found to agree with our nuclear
$\sigma_{\ast}$ measurement for NGC4459, for NGC4435 the observed
$\sigma_{\ast}$ is remarkably smaller than the predicted one, which further
suggests that this galaxy could host an undermassive SBH.
