Matrix metalloproteinases are a family of Zn-proteases involved in tissue remodeling and in many pathological conditions. Among them MMP-2 is one of the most relevant target in anticancer therapy. Commonly, MMP inhibitors contain a functional group able to bind the zinc ion and responsible for undesired side effects. The discovery of potent and selective MMP inhibitors not bearing a zinc-binding group is arising for some MMP family members and represents a new opportunity to find selective and non toxic inhibitors.In this work we attempted to get more insight on the inhibition process of MMP-2 by two non-zinc-binding inhibitors, applying a general protocol that combines several computational tools (docking, Molecular Dynamics and Quantum Chemical calculations), that all together contribute to rationalize experimental inhibition data. Molecular Dynamics studies showed both structural and mechanical-dynamical effects produced by the ligands not disclosed by docking analysis. Thermodynamic Integration provided relative binding free energies consistent with experimentally observed activity data. Quantum Chemical calculations of the tautomeric equilibrium involving the most active ligand completed the picture of the binding process. Our study highlights the crucial role of the specificity loop and suggests that enthalpic effect predominates over the entropic one.