In this work, the authors report the operation of a cylindrical dielectric resonator antenna (CDRA) in the high gain HEM13δ mode, for the first time. This mode, excited with a standard microstrip slot, radiates in the broadside direction with gain in the range of 8−10 dBi. It is shown that through feed optimization, the HEM13δ mode can be excited dominantly by suppressing the fundamental HEM11δ mode of the CDRA. Detailed simulation studies show that the HEM13δ mode is supported by cylindrical dielectric resonators with an aspect ratio (radius to height ratio or a/d) >1, and it resonates at a frequency approximately 2.2 times that of the fundamental HEM11δ mode. The above features of the HEM13δ mode CDRA can be used as approximate design rules. For a CDRA with dielectric constant ɛr = 24, diameter 2a = 19.43 mm, and height d = 7.3 mm (a/d = 1.3), the HEM13δ mode is excited at 6.125 GHz with a peak gain of 10.14 dBi in simulation. Corresponding values from prototype measurement are 5.981 GHz and 9.62 dBi, respectively for the resonant frequency and the gain, verifying the simulation.