A new geometry of compact wideband/dual‐band circularly polarised dielectric resonator antenna (DRA) is presented. First, a wideband DRA is realised by a rectangular dielectric resonator excited by a vertical coaxial probe feed which is supported by a small substrate. Circular polarisation is achieved by utilising a configuration of the DRA feed that excites orthogonal modes inside the DRA. A 3 dB axial‐ratio bandwidth of about 20.8% (9.05–11.14 GHz) is achieved. Second, extension to dual‐band circularly polarised operation is then realised by additionally removing a corner of the rectangular DRA at 45° and adding a floating parasitic strip. The experimental results demonstrate an impedance bandwidth of about 59.8% (6.57–12.18 GHz) and the dual 3 dB axial‐ratio bandwidths of about 10.6% (8.31–9.24 GHz) and 13.5% (10.18–11.66 GHz). The measured peak gain varies from 4.47 to 4.86 dBiC in the lower band and 4.33 to 4.91 dBiC in the upper band.