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In this letter, we propose a resonant approach to achieve enhanced power transmission through electrically small apertures in the near-infrared. The enhancement is obtained by exciting a magnetic resonance in a pair of plasmonic pillars, placed on a screen with a drilled subwavelength hole. The localized resonance allows us to enhance the equivalent magnetic dipole moment of the aperture, hence increasing the transmitted power. The proposed setup may find interesting applications in high-capacity memories, ultradiffractive imaging systems, high-resolution spatial filters, and high-precision lithography.