The accuracy of determination of tensor parameters measured using solid-state nuclear magnetic resonance is investigated. In particular, the reliability of the determination of the anisotropy and the asymmetry parameter of the chemical shift is calculated using the Cramer-Rao lower bounds. Minimizing this measure of the error as a function of an experimental parameter (in this case the spinning speed of the sample) enables the optimization of any given experiment. Hence, an optimum number of sidebands is found for which the determination of the anisotropy is most reliable. Comparision to the static limit shows that the reliability of the determination of the anisotropy is always greater in spinning experiments than in static experiments. An analogous analysis for the asymmetry parameter shows it to be consistently more reliably determined from a static spectrum. The sensitivity of the fitting to the simulation algorithm is found to become pronounced with slower speeds and static spectra, and a discussion of such systematic errors is provided. The reliability of the determination of dipolar or first-order quadrupolar tensors is also calculated, and we find that this presents a surprisingly different situation to that of the chemical shift. (C) 1997 American Institute of Physics.