Calculations of the energies and the nuclear magnetic resonance chemical shieldings have been performed on the (HF)2 and (H2O)2 van der Waals dimers as a function of the key interdimer geometric variables. 6-311 G-(d,p) and 6-311++G(2d,2p) bases have been employed at the SCF and MP2 levels, both with and without the functional counterpoise correction for basis set superposition error (bsse). Chemical shieldings were determined by using the gauge including atomic orbital (GIAO) method. Proton shielding changes are large and generally parallel the energy changes when the angular variables are modified, while the fluorine and oxygen changes are more complex; there is no correlation of any of the shielding changes with the energy for modification of the interdimer distance. Chemical shielding counterpoise corrections are negligible for hydrogen but are quite sizeable for the heavy atoms in the smaller basis without diffuse functions. Not only does the presence of diffuse functions in the larger basis set reduce the energy bsse considerably, but it virtually obviates the need for counterpoise corrections for the chemical shieldings of the heavy atoms.