Mercury(IV) fluoride, HgF4, is thermodynamically stable or only slightly endothermic with respect to gaseous HgF2 + F2 and might be accessible via fluorination of HgF2, e.g. by KrF2. This is the result of high-level quasirelativistic pseudopotential QCISD(T) calculations. In contrast, the existence of CdF4 is unlikely and that of ZnF4 even more so. The easier oxidation of HgF2, compared to CdF2 or ZnF2, is due to a relativistic destabilization of the Hg(II)-F bonds rather than to a relativistic stabilization of HgF4. Spin-orbit coupling also contributes to a stabilization of HgF4 vs HgF2 + F2, but only slightly. The performance of various computational levels to treat electron correlation and of a general basis-set contraction scheme based on atomic natural orbitals have been evaluated. The characterization of molecular HgF4 should be possible via vibrational spectroscopy, as the calculated harmonic frequencies differ considerably from those of other possible species that might be present in the reaction mixture. Calculations on anionic model complexes and on the dimers (HgF4)2 and (HgF2)2 show that HgF4 gains only limited additional stability by anionic complexation or by aggregation. Thus, any successful synthesis should involve conditions where the lattice energy of HgF2 is not relevant (e.g. gas-phase molecular beam experiments or reactions in solution).