Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for non-relativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the 4-component Dirac-Coulomb Hamiltonian using Dyall’s acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with non-relativistic CCSD(T) calculations using the very large polarization-consistent basis sets aug-pcSseg-4 for He, Ne and Ar, aug-pcSseg-3 for Kr and the AQZP basis set for Xe. For the dimers also zero-point vibrational corrections obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, zero-point vibrational and relativistic corrections for the shieldings and chemical shifts is analyzed.