Extremely wideband resonant cavity antennas (RCAs) with large directivity-bandwidth products (DBPs) are presented. Their distinct feature is a single-slab superstrate that has a permittivity gradient in the directions transverse to the antenna axis. The application of such a superstrate in a single-feed RCA improves the DBP by a factor of three or more as compared with superstrates composed of uniform dielectric slabs. Their very small area enables an antenna designer to achieve unprecedented figures of DBP per unit area, from a simple planar antenna. Prototype RCAs have been fabricated and measurements have validated the concept. A measured 3-dB directivity bandwidth of 52.9% was demonstrated with a measured directivity of 16.4 dBi for an RCA that has a very small total footprint area of 1.54λ²₀ at the lowest operating frequency (2.84λ²₀,c at the center frequency). This represents an increase of 90% over the previous best measured RCA directivity bandwidth of 28%.