Available experimental data for the active sites of the hydroxylase component of methane monooxygenase (MMOH) and the R2 subunit of ribonucleotide reductase (R2) indicates high flexibility of the ligand environment of the iron centers in these two metalloproteins, suggesting that carboxylate ligands may play a special role for proper enzymatic functioning. By using quantum chemical methods, here we have investigated (1) the so-called 1,2-carbosylate shift (i.e., shift of a bridging carboxylate ligand from mu -1,1 to mu -1,2 between two metal centers), and (2) the monodentate <-> bidentate rearrangement of terminal carboxylate ligands (bound to only one metal center), in the reduced forms of MMOH and R2. Our results show that (i) MMOH-like and R2-like structures, with a mu -1,1 and mu -1,2 bridged carboxylate ligand, respectively, are energetically very close; (ii) complexes with lower coordination numbers in the Fe-2 center are computed to be slightly more stable than those with higher coordination numbers, and (nl) the two studied carboxylate shifts are easy processes, not only thermodynamically but also kinetically, with activation barriers of only a few kcal/mol. Our conclusion that the carboxylate ligands of dinuclear complexes such as MMOHred and R2(red) are very flexible is in a good agreement with the available experimental data.