In this paper, two H‐plane horn antennae are designed using groove and ridge gap waveguide (GGW and RGW) techniques. In the proposed structures, the gap waveguide is partially filled with a dielectric to control the amplitude and phase distribution across the antenna aperture so that a very low side lobe level (SLL) can be achieved. Two sample antennae are designed and simulated for the frequency range from 12 to 16 GHz, and the prototypes are fabricated. The fabricated antennae show quite wide impedance bandwidth (S11 ≤ 10 dB) of 28% and 32% for the RGW and GGW versions, respectively. The obtained maximum side lobe level for the designed GGW and RGW horns is about −30 and −24 dB, respectively, over the operating bandwidth. In comparison with state‐of‐the‐art designs, the proposed structures introduce much lower SLL.