We have measured the Stokes drag on magnetic nanowires suspended in the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB). The effective drag viscosity for wires moving perpendicular to the nematic director differs from that for motion parallel to the director by factors of 0.88 to 2.4, depending on the orientation of the wires and their surface anchoring. When the force on the wires is applied at an oblique angle to the director, the wires move at an angle to the force, demonstrating the existence of a lift force on particles moving in a nematic. This dynamic lift is significantly larger for wires with homeotropic anchoring than with longitudinal anchoring in the experiments, suggesting the lift force as a mechanism for sorting particles according to their surface properties.