The 13C NMR chemical shifts for functionalized (7,0), (8,0), (9,0), and (10,0) single-walled carbon nanotubes (SWNTs) have been studied computationally using gauge-including projector-augmented plane-wave (GIPAW) density functional theory (DFT). The functional groups NH, NCH3, NCH2OH, and CH2NHCH2 have been considered, and different sites where covalent addition or substitution may occur have been examined. The shifts of the carbons directly attached to the group are sensitive to the bond which has been functionalized and may, therefore, be used to identify whether the group has reacted with a parallel or a diagonal C-C bond. The addition of NH to a parallel bond renders the functionalized carbons formally sp3-hybridized, yielding shifts of around 44 ppm, independent of the SWNT radius. Reaction with a diagonal bond retains the formal sp2 hybridization of the substituted carbons, and their shifts are slightly lower or higher than those of the unsubstituted carbon atoms. The calculated 1H NMR shifts of protons in the functional groups are also dependent upon the SWNT-group interaction. Upon decreasing the degree of functionalization for the systems where the group is added to a parallel bond, the average chemical shift of the unfunctionalized carbons approaches that of the pristine tube. At the same time, the shifts of the functionalized carbons remain independent upon the degree of functionalization. For the SWNTs where N-R attaches to a parallel bond, the average shift of the sp2 carbons was found to be insensitive to the substituent R. Moreover, the shifts of the functionalized sp3 carbons, as well as of the carbons within the group itself, are independent of the SWNT radius. The results indicate that a wealth of knowledge may be obtained from the 13C NMR of functionalized SWNTs.