In the present study, a theoretical investigation of the potential of various metal-functionalized R-substituted pyrogallolarenes (i.e., M-R-Pygarene; M=Li+, K+, Na+ and Mg2+; R=methyl and fluoroethyl) as media for molecular hydrogen (H2) storage is reported. Initially, the structural features of the metal-functionalized systems are obtained at the B3LYP/6-311G(d,p) level of theory. Subsequently, the interaction of a H2 molecule with the cations embedded in the cavity of the macrocyclic molecules is described with the B3LYP functional using two basis sets of different flexibility, namely BSA: 6-311G(d,p) for all atoms, and BSB: 6-311G(d,p) and aug-cc-pVDZ for M-R-Pygarene and H2, respectively. Notably large BSSE-corrected binding energy values were obtained at the B3LYP/BSB level for the different H2/M-R-Pygarene complexes spanning the 1.3-17.0kJ/mol range. The resulting values were further refined through two approaches: (i) by employing the functional B97D, which includes a Grimme's type correction for describing dispersive forces and (ii) by performing MP2 calculations within the frame of the ONIOM approach. Binding energies refined at the MP2 level resulted in an average increment of about ~2.5kJ/mol when considering all the complexes under investigation. On the other hand, B97D binding energies were found to be overestimated since too large increments (i.e., three- and fourfold with respect to B3LYP values for the case of Li- and Na-functionalized systems, respectively) were observed. For the specific case of the H2/Mg-fluoroethyl-Pygarene, an adsorption enthalpy (δHads0) of -17.6kJ/mol was estimated by adding the zero point energy and thermal effects computed at 300K from harmonic vibrational frequencies, obtained at the B3LYP/BSB level. This relatively high adsorption enthalpy suggests that Mg-functionalized R-Pygarenes can be envisaged as promising systems for molecular hydrogen storage.