One factor that can strongly influence predicted free energy of binding is the ionization state of functional groups on the ligands and at the binding site at which calculations are performed. This analysis is seldom performed except in very detailed computational simulations. In this work, we address the issues of (i) modeling the complexity resulting from the different ionization states of ligand and protein residues involved in binding, (ii) if, and how, computational methods can evaluate the pH dependence of ligand inhibition constants, and (iii) how to score the protonation-dependent models. We developed a new and fairly rapid protocol called "computational titration" that enables parallel modeling of multiple ionization ensembles for each distinct protonation level. Models for possible protonation combinations for site/ligand ionizable groups are built, and the free energy of interaction for each of them is quantified by the HINT (Hydropathic INTeractions) software. We applied this procedure to the evaluation of the binding affinity of nine inhibitors (six derived from 2,3-didehydro-2-deoxy-N-acetylneuraminic acid, DANA) of influenza virus neuraminidase (NA), a surface glycoprotein essential for virus replication and thus a pharmaceutically relevant target for the design of anti-influenza drugs. The three-dimensional structures of the NA enzyme-inhibitor complexes indicate considerable complexity as the ligand-protein recognition site contains several ionizable moieties. Each computational titration experiment reveals a peak HINT score as a function of added protons. This maximum HINT score indicates the optimum pH (or the optimum protonation state of each inhibitor-protein binding site) for binding. The pH at which inhibition is measured and/or crystals were grown and analyzed can vary from this optimum. A protonation model is proposed for each ligand that reconciles the experimental complex structure with measured inhibition and the free energy of binding. Computational titration methods allow us to analyze the effect of pH in silico and may be helpful in improving ligand binding free energy prediction when protonation or deprotonation of the residues or ligand functional groups at the binding site might be significant.