We present new measurements for the nuclear stellar velocity dispersion sigma(*) 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(*) measurements can be useful for constraining the mass M-circle of supermassive black holes (SBHs) by concentrating on the cases of the lenticular galaxies NGC 4435 and NGC 4459. These are characterized by similar ground-based half-light radii stellar velocity dispersion sigma(e) values but remarkably different M-circle as obtained from modelling their central ionized-gas kinematics, where NGC 4435 appears to host a significantly undermassive SBH compared to what is expected from the M-circle - sigma(e) relation. For both galaxies, we build Jeans axisymmetric dynamical models to match the ground-based stellar kinematics obtained with Spectrographic Areal Unit for Research on Optical Nebulae integral-field spectrograph, including an SBH with M-circle value as predicted by the M-circle - sigma(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(+) value. Whereas this was found to agree with our nuclear sigma(+) measurement for NGC 4459, for NGC 4435 the observed sigma(*) is remarkably smaller than the predicted one, which further suggests that this galaxy could host an undermassive SBH.