This mini-review reports supramolecular system composed of O-methylated beta-cyclodextrins and metalloporphyrins that mimic the functions of myoglobin (Mb) in aqueous solution. Although many Mb functional models have been demonstrated so far, most models can bind dioxygen only in organic solvents such as toluene. Recently, we prepared the model systems composed of O-methylated beta-cyclodextrin dimers having pyridine and imidazole linkers and tetrakis(4-sulfonatophenyl)porphinato iron(II) (hemoCD and Fe(II)PImCD). HemoCD binds dioxygen reversibly in aqueous solution, and the dioxygen adduct of hemoCD is very stable (a half-lifetime is 30 h at pH 7). Although the dioxygen affinity of Fe(II)PImCD is much higher than hemoCD, the stability and the reversibility of this system is lower. This review compares the functions of these model systems with those in biological systems.