We present predictions of neutron relative biological effectiveness (RBE) for cell irradiations with neutron beams at PTB-Braunschweig. A neutron RBE model is adopted to evaluate initial DNA damage induction given the neutron-induced charged particle field. RBE values are predicted for cell exposures to quasi-monoenergetic beams (0.56 MeV, 1.2 MeV) and to a broad energy distribution neutron field with dose-averaged energy of 5.75 MeV. Results are compared to what obtained with our RBE predictions for neutrons at similar energies, when a 30-cm sphere is irradiated in an isotropic neutron field. RBE values for experimental conditions are higher for the lowest neutron energies, because, as expected, target geometry determines the weight of the low-effectiveness photon component of the neutron dose. These results highlight the importance of characterizing neutron fields in terms of physical interactions, to fully understand neutron-induced biological effects, contributing to risk estimation and to the improvement of radiation protection standards.