Ultra-compact high velocity clouds (UCHVCs) were identified in the ALFALFA HI survey as potential gas-bearing dark matter halos. Here we present higher resolution neutral hydrogen (HI) observations of twelve UCHVCS with the Westerbork Synthesis Radio Telescope (WSRT). The UCHVCs were selected based on a combination of size, isolation, large recessional velocity and high column density as the best candidate dark matter halos. The WSRT data were tapered to image the UCHVCs at 210" (comparable to Arecibo) and 105" angular resolution. In a comparison of the single-dish to interferometer data, we find that the line flux recovered in the WSRT observations is comparable to that from the single-dish ALFALFA data. In addition, any structure seen in the ALFALFA data is reproduced in the WSRT maps at the same angular resolution. At 21" resolution all the sources are generally compact with a smooth HI morphology, as expected from their identification as UCHVCs. At the higher angular resolution, a majority of the sources break into small clumps contained in a diffuse envelope. These UCHVCs also have no ordered velocity motion and are most likely Galactic halo clouds. We identify two UCHVCs, AGC 198606 and AGC 249525, as excellent galaxy candidates based on maintaining a smooth HI morphology at higher angular resolution and showing ordered velocity motion consistent with rotation. A third source, AGC 249565, lies between these two populations in properties and is a possible galaxy candidate. If interpreted as gas-bearing dark matter halos, the three candidate galaxies have rotation velocities of 8-15 km/s(-1), HI masses of 0.6-50 x 10(5) M-circle dot, HI radii of 0.3-2 kpc, and dynamical masses of 2-20 x 10(7) M-circle dot for a range of plausible distances. These are the UCHVCs with the highest column density values in the ALFALFA HI data and we suggest this is the best way to identify further candidates.