The reaction of hydrogen sulfide (H2S) with hemeproteins is a key physiological reaction; still, its mechanism and implications are not completely understood. In this work, we propose a combination of experimental and theoretical tools to shed light on the reaction in model system microperoxidase 11 (MP11-FeIII) and myoglobin (Mb-FeIII), from the estimation of the intrinsic binding constants of the species H2S and hydrosulfide (HS-), and the computational description of the overall binding process. Our results show that H2S and HS- are the main reactive species in Mb-FeIII and MP11-FeIII, respectively, and that the magnitude of their intrinsic binding constants are similar to most of the binding constants reported so far for hemeproteins systems and model compounds. However, while the binding of HS- to Mb-FeIII was negligible, the binding of H2S to MP11-FeIII was significant, providing a frame for a discriminated analysis of both species and revealing differential mechanistic aspects. A joint inspection of the kinetic data and the free energy profiles of the binding processes suggests that a dissociative mechanism with the release of a coordinated water molecule as rate limiting step is operative in the binding of H2S to Mb-FeIII and that the binding of HS- is prevented in the access to the protein matrix. For the MP11-FeIII case, where no access restrictions for the ligands are present, an associative component in the mechanism seems to be operative. Overall, the results suggest that if accessing the active site then both H2S and HS- are capable of binding a ferric heme moiety.