Shimming systems are required to provide sufficient field homogeneity for high resolution NMR. In certain specialized applications, such as rotating-field NMR and portable (ex-situ) NMR, permanent magnet-based shimming systems can provide considerable advantages. We present a simple two-dimensional shimming method based on harmonic corrector rings which can provide arbitrary multipole order shimming corrections. Results demonstrate, for example, that quadrupolar order shimming improves the linewidth by up to an order of magnitude. An additional order of magnitude reduction is in princliple achievable by ultilizing this shimming method for z-gradient correction and higher order xy gradients
