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A metamaterial paradigm for achieving an efficient, electrically small antenna is introduced. Spherical shells of homogenous, isotropic negative permittivity (ENG) material are designed to create electrically small resonant systems for several antennas: an infinitesimal electric dipole, a very short center-fed cylindrical electric dipole, and a very short coaxially-fed electric monopole over an infinite ground plane. Analytical and numerical models demonstrate that a properly designed ENG shell provides a distributed inductive element resonantly matched to these highly capacitive electrically small antennas, i.e., an ENG shell can be designed to produce an electrically small system with a zero input reactance and an input resistance that is matched to a specified source resistance leading to overall efficiencies approaching unity. Losses and dispersion characteristics of the ENG materials are also included in the analytical models. Finite element numerical models of the various antenna-ENG shell systems are developed and used to predict their input impedances. These electrically small antenna-ENG shell systems with idealized dispersionless ENG material properties are shown to be very efficient and to have fractional bandwidths above the values associated with the Chu limit for the quality factor without any degradation in the radiation patterns of the antennas. Introducing dispersion and losses into the analytical models, the resulting bandwidths are shown to be reduced significantly, but remain slightly above (below) the corresponding Chu-based value for an energy-based limiting (Drude) dispersion model of the permittivity of the ENG shell.