The RNA-dependent RNA polymerase (RdRp) of norovirus is an attractive target of antiviral agents aimed at providing protection against norovirus-associated gastroenteritis. Here, we perform molecular dynamics simulations of the crystal structure of norovirus RdRp in complex with several known binders, as well as free-energy simulations by free-energy perturbation (FEP) to determine binding free energies of these molecules relative to the natural nucleotide substrates. We determine experimental EC50 values and nucleotide incorporation efficiencies for several of these compounds. Moreover, we investigate the mechanism of inhibition of some of these ligands. Using FEP, we screened a virtual nucleotide library with 121 elements for binding to the polymerase and successfully identified two novel chain terminators.