Both solid-state and solution NMR relaxation measurements are routinely used to quantify the internal dynamics of biomolecules, but in very few cases have these two techniques been applied to the same system, and even fewer attempts have been made so far to describe the results obtained through these two methods through a common theoretical framework. We have previously collected both solution 13C and solid-state 2H relaxation measurements for multiple nuclei within the furanose rings of several nucleotides of the DNA sequence recognized by HhaI methyltransferase. The data demonstrated that the furanose rings within the GCGC recognition sequence are very flexible, with the furanose rings of the cytidine, which is the methylation target, experiencing the most extensive motions. To interpret these experimental results quantitatively, we have developed a dynamic model of furanose rings based on the analysis of solid-state 2H line shapes. The motions are modeled by treating bond reorientations as Brownian excursions within a restoring potential. By applying this model, we are able to reproduce the rates of 2H spin-lattice relaxation in the solid and 13C spin-lattice relaxation in solution using comparable restoring force constants and internal diffusion coefficients. As expected, the 13C relaxation rates in solution are less sensitive to motions that are slower than overall molecular tumbling than to the details of global molecular reorientation, but are somewhat more sensitive to motions in the immediate region of the Larmor frequency. Thus, we conclude that the local internal motions of this DNA oligomer in solution and in the hydrated solid state are virtually the same, and we validate an approach to the conjoint analysis of solution and solid-state NMR relaxation and line shapes data, with wide applicability to many biophysical problems.