The C-13 NMR analysis of relaxation data from viscous solutions requires the application of complex mathematical functions. These equations can be combined and solved exactly using a series of iterative algorithms. Correct analysis of typical relaxation data obtained for several viscous ionic liquids provides rotational correlation times that describe the molecular dynamics of these and other viscous solutions. The C-13 NMR relaxation data for 1-methyl-3-nonyl-imidazolium PF6 ionic liquid is used to illustrate the details of this method using iterative techniques in a stepwise manner. This approach is outlined such that other investigators can easily duplicate the algorithms.