The gain of a standard rectangular dielectric resonator antenna (DRA) is enhanced by integrating it with a surface mounted short horn (SMSH). An enhancement of gain by 3.7 dB to 9.8 dBi at 5.95 GHz, and a 10 dB return bandwidth of 3.2% has been achieved from this configuration. Performances of antennas with different types of SMSHs are studied; SMSHs made out of thin metal strips or strips supported by foam are found to be best. Next, the bandwidth of the antennas is enhanced by replacing the DRA with a wideband hybrid antenna, consists of a rectangular DR on a patch resonator. A return loss bandwidth of 25%, and a gain better than 8.5 dBi over this bandwidth, has been achieved. The boresight cross-polarisation level is less than 227 dB and the sidelobe level is less than 215 dB over the entire bandwidth.