Keck/LRIS multi-object spectroscopy has been carried out on 140 of some of the lowest and highest surface brightness faint (19 < R < 22) dwarf galaxy candidates in the core region of the Coma Cluster. These spectra are used to measure redshifts and establish membership for these faint dwarf populations. The primary goal of the low surface brightness sample is to test our ability to use morphological and surface brightness criteria to distinguish between Coma Cluster members and background galaxies using high resolution HST/ACS images. Candidates were rated as expected members, uncertain, or expected background. From 93 spectra, 51 dwarf galaxy members and 20 background galaxies are identified. Our morphological membership estimation success rate is ~100% for objects expected to be members and better than ~90% for galaxies expected to be in the background. We confirm that low surface brightness is a very good indicator of cluster membership. High surface brightness galaxies are almost always background with confusion arising only from the cases of the rare compact elliptical galaxies. The more problematic cases occur at intermediate surface brightness. Many of these galaxies are given uncertain membership ratings, and these were found to be members about half of the time. Including color information will improve membership determination but will fail for some of the same objects that are already mis-identified when using only surface brightness and morphology criteria. Compact elliptical galaxies with B-V colors ~0.2 magnitudes redward of the red sequence in particular require spectroscopic follow-up. In a sample of 47 high surface brightness, UCD candidates, 19 objects have redshifts which place them in the Coma Cluster. Redshift measurements are presented and the use of indirect means for establishing cluster membership is discussed.
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