Two years ago, the OGLE-III survey (Optical Gravitational Lensing Experiment) announced the detection of 54 short period multi-transiting objects in the Galactic bulge (Udalski et al., 2002a, 2002b). Some of these objects were considered to be potential hot Jupiters. In order to determine the true nature of these objects and to characterize their actual mass, we conducted a radial velocity follow-up of 18 of the smallest transiting candidates. We describe here our procedure and report the characterization of 8 low mass star transiting companions, 2 grazing eclipsing binaries, 2 triple systems, 1 confirmed exoplanet (OGLE-TR-56b), 1 possible exoplanet (OGLE-TR-10b), 1 clear false positive and 3 unsolved cases. The variety of cases encountered in our follow-up covers a large part of the possible scenarii occuring in the search for planetary transits. As a by-product, our program yields precise masses and radii of low mass stars.