We summarize results from an extensive search for HI 21cm absorption at moderate redshifts. The survey was limited to systems with Mg II absorption at redshifts in the range 0.2 < z < 1.0, which lie in front of bright radio quasars. Narrow band observations centered at the metalline redshifts were made with the UHF-high system and, when possible, the DZB correlator at the WSRT. Three new absorbers have been confirmed and several candidate absorbers identified. Optical depth limits of a few percent at velocity resolutions of about 6 km s−1 are obtained for most of the non-detections. The 21cm search is complementary to similar damped Lyα surveys, and by combining information from both absorption lines we are able to better understand physical conditions in these high neutral column density absorbers. We find that the 21cm objects represent a cold subset of high neutral column density absorbers, but are not necessarily the highest column density systems.