We present a novel method for obtaining high resolution NMR spectra in the presence of grossly inhomogeneous magnetic fields, such as those encountered in one-sided access NMR. Our method combines the well-known principle of reference deconvolution with NMR imaging in order to resolve spectral features with frequency resolution orders of magnitude smaller than the prevailing line-broadening due to field inhomogeneity. We demonstrate that, in cases of inhomogeneous field line-broadening more than an order of magnitude larger than the spectral features to be resolved, rather than performing reference deconvolution on the sample as a whole, it is more favourable in terms of SNR to divide the target region of a sample into smaller sub-regions, by means of chemical shift imaging, and then to perform reference deconvolution on the individual sub-region spectra, finally summing the results In this way, significant resolution enhancements can be obtained in the presence of severe magnetic field inhomogeneity without an unacceptable loss in SNR.