We present theory to describe the plasmonic resonances of a subwavelength annular aperture in a real metal plate. The theory provides the reflection, including the amplitude and phase, of radially polarized surface plasmon waves from the end faces of the aperture with a significant departure from the perfect electric conductor case due to plasmonic effects. Oscillations in the reflection amplitude and phase are observed. These oscillations arise from transverse resonances and depend on the geometry of the annulus. The theory is applied to the design of various aperture structures operating at the same resonance wavelength, and it is confirmed by comprehensive electromagnetic simulations. The results are contrasted to the perfect electric conductor case and they will be of significant interest to emerging applications in metamaterials, plasmonic sensors, and near-field optics.