We present a method to evaluate the free energies of ligand binding utilizing a Monte Carlo estimation of the configuration integrals concomitant with uncertainty quantification. Ensembles for integration are built through systematically perturbing an initial ligand conformation in a rigid binding pocket, which is optimized separately prior to incorporation of the ligand. We call the procedure producing the ensembles "blurring", and it is carried out using an in-house developed code. The Boltzmann factor contribution of each pose to the configuration integral is computed and from there the free energy is obtained. Potential function uncertainties are estimated using a fragment-based error propagation method. This method has been applied to a set of small aromatic ligands complexed with T4 Lysozyme L99A mutant. Microstate energies have been determined with the force fields ff99SB and ff94, and the semiempirical method PM6DH2 in conjunction with continuum solvation models including Generalized Born (GB), the Conductor-like Screening Model (COSMO), and SMD. Of the methods studied, PM6DH2-based scoring gave binding free energy estimates, which yielded a good correlation to the experimental binding affinities (R (2) = 0.7). All methods overestimated the calculated binding affinities. We trace this to insufficient sampling, the single static protein structure, and inaccuracies in the solvent models we have used in this study.