Thrombin is a serine protease responsible for blood coagulation. Since thrombin inhibitors appear to be effective in the treatment and prevention of thrombotic and embolic disorders, considerable attention has been focused on the structure and interactions of this enzyme. Here, to evaluate the relative free energies of hydration and binding to thombin between two serine protease inhibitors, p-methylbenzamidine and benzamidine, we employed molecular dynamics simulations in conjunction with free-energy perturbation calculations. To accomplish that, we used the finite difference thermodynamic integration (FDTI) algorithm within the Discover program of MSI. We have shown the importance of the inclusion of intraperturbed-group contributions to the free energy, and demonstrated that the orthogonality problem that occurs in the calculation of these contributions is adequately treated by the FDTI method. We have also demonstrated that problems of singularity and convergence in free-energy calculations can be properly solved by combining the FDTI method with the Gaussian-Legendre quadrature method for numerical integration, associated with the introduction of a physical criterion to determine the breaking point of a bond or angle described by a harmonic potential. The results seem to indicate that the greater affinity of p-methylbenzamidine for thrombin is derived from stronger electrostatic and hydrophobic interactions between this molecule and the enzyme.