From a search of a portion of the sky covered by the SDSS and UKIDSS databases, we have located 2 galaxies at z~0.5 that have properties similar to those of the luminous passive compact galaxies found at z~2.5. From Keck moderate-resolution spectroscopy and laser-guided adaptive-optics imaging of these galaxies, we can begin to put together a more detailed picture of what their high-redshift counterparts might be like. Spectral-synthesis models that fit the u to K photometry also seem to give good fits to the spectral features. From these models, we estimate masses in the range of 3-4 10^11 M_sun for both galaxies. Under the assumption that these are spheroidal galaxies, our velocity dispersions give estimated masses about a factor of 3 smaller. However, our high-resolution imaging data indicate that these galaxies are not normal spheroids, and the interpretation of the kinematic data depends critically on the actual morphologies and the nature of the stellar orbits. While recent suggestions that the population of high-redshift compact galaxies is present locally as the inner regions of local massive elliptical galaxies are quite plausible, the peak mass surface densities of the two galaxies we discuss here appear to be up to a factor of 10 higher than those of the highest density local ellipticals, assuming that our photometric masses are roughly correct. It thus seems possible that some dynamical "puffing-up'' of the high-redshift galaxies might still be required in this scenario.