Theoretical calculations of the chemical shielding tensor using the coupled Hartree-Fock and localized orbital methods with different basis sets are compared for the ethylenic carbon atoms, which are expected to have a large antisymmetric component, in tetrachlorocyclopropene, tetrafluorocyclopropene, dichlorocyclopropene and cyclopropene at optimized geometries. Two modest attempts, made to extrapolate these results to the Hartree-Fock limit, demonstrate that the LORG method gives the most reliable calculated results but that there is still much room for improvement. Comparison of the calculated value of the antisymmetric component of the shielding tensor for tetrachlorocyclopropene agrees approximately with the experimental value.