We present a detailed analytical theory for the plasmonic nanoring configuration first proposed by Alù et al. [Opt. Express 14, 1557 (2006)], which is shown to provide negative magnetic permeability and negative index of refraction at infrared and optical frequencies. We show analytically how the nanoring configuration may provide superior performance when compared to some other solutions for optical negative-index materials, offering a more "pure" magnetic response at these high frequencies, which is necessary for lowering the effects of radiation losses and absorption. Sensitivity to losses and the bandwidth of operation of this magnetic inclusion are also investigated in detail and compared with other available setups.