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The resonance performance and Q-factor of electrically small ellipsoidal radiators made of epsilon negative (ENG) material is investigated. It is demonstrated that the material polarization can successfully provide resonance radiation at the negative material constitutive parameters. In principle, arbitrary low resonant frequencies for a fixed antenna dimension can be achieved. The dependence of resonant frequency on the shape of the structure is determined. Special attention is devoted to the sphere, thin disk, and long rod, and physical insights into the radiation characteristics and Q (or bandwidth) are highlighted.