This paper represents the second part of a study of solvation of peptides. As in the first part, N-methyl acetamide has been used to model the specific features of solvation of the peptide linkage. In this part of the study, devoted to nuclear magnetic shieldings, acetone and water have been used as examples of polar and/or hydrogenbond donor/acceptor solvents. Once again, three different solvation models have been tested and compared, namely, a continuum only description, a discrete description in terms of solute-solvent clusters, and a mixed discrete/continuum description in terms of clusters embedded in a continuum. Both QM and classical simulation (e.g., MD) approaches have been used to determine the structure of the clusters. The analysis of the results of the three different models, when combined with those obtained in the first part of the study devoted to IR and UV spectra, has allowed us to identify and characterize different aspects of solvation and to outline a possible computational strategy to describe dynamic and static effects due to bulk and specific peptide-solvent interactions.