Expressions are derived within the relativistic regular approximation (ZORA) for the evaluation of the magnetic hyperfine interactions in paramagnetic molecules. For hydrogen-like atoms exact first order relations between the ZORA and Dirac formalism are given for the calculation of g- and A-tensors. Density functional calculations are performed on the neutral atoms Cu, Ag and Au, on some small test molecules NO2, HCO, and TiF3, and on some paramagnetic clusters consisting of 5 or 7 atoms of the group IB metals : Cu-7, Cu2Ag5, CuAg6, Ag-5, Ag-7, and Au-7. It is shown that the calculated ESR parameters of the heptamers are in good agreement with results of experiments, which originally were assigned to pentamers.