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We address the question of the optimal choice of loading material for antenna miniaturization. A new approach to identify the optimal loading material (dielectric or magnetic) for maximization of bandwidth of resonant antennas is introduced. Instead of equivalent resonant circuits or transmission-line resonators, we use the analysis of radiation mechanism to identify the fields contributing mostly to the stored energy and determine the beneficial material type. The formulated rule is qualitatively illustrated using a dipole and a patch antenna, as well as a planar inverted-L antenna where the conventional analysis of circuit or a transmission-line resonator leads to incorrect conclusions. Guidelines are presented for miniaturizing different antenna types.