  Observational measurements of the relationship between supermassive black
holes (SMBHs) and the properties of their host galaxies are an important method
for probing theoretical hierarchical growth models. Gravitational lensing is a
unique mechanism for acquiring this information in systems at cosmologically
significant redshifts. We review the calculations required to include SMBHs in
two standard galactic lens models, a cored isothermal sphere and a broken power
law. The presence of the SMBH produces two primary effects depending on the
lens configuration, either blocking the ``core'' image that is usually
predicted to form from a softened lens model, or adding an extra, highly
demagnified, image to the predictions of the unaltered lens model. The
magnitudes of these effects are very sensitive to galaxy core sizes and SMBH
masses. Therefore, observations of these lenses would probe the properties of
the inner regions of galaxies, including their SMBHs. Lensing cross-sections
and optical depth calculations indicate that in order to fully observe these
characteristic signatures, flux ratios of order 10^6 or more between the
brightest and faintest images of the lens must be detectable, and thus the next
generation of radio telescope technology offers the first opportunity for a
serious observational campaign. Core images, however, are already detectable
and with additional observations their statistics may be used to guide future
SMBH searches.
