1. A method for grading the cut of a physical or virtual gemstone, comprising receiving cut proportions for the gemstone; obtaining scores for a plurality of cut score components, including accessing prediction tables from which scores for designated ones of the plurality of cut score components can be obtained, and in which each of the designated cut score components has an associated range of possible scores, wherein, for a particular designated cut score component, the possible scores are associated with corresponding ranges of cut proportions, and the corresponding ranges are based upon theoretically derived scores combined with empirically derived boundaries or thresholds, wherein the theoretically derived scores have been determined for possible cut proportions for the particular designated cut score component, and the boundaries or thresholds have been set by statistical analysis of observations of the particular designated cut score component; applying the received cut proportions to the accessed prediction tables to obtain corresponding scores for the designated cut score components; and outputting the cut grade reports for the gemstone.