The spectrum of secondary neutrons generated by a medical linear accelerator (linac) during high-energy radiation therapy must be accurately determined in order to assess the carcinogenic risk that these neutrons pose to patients. Neutron spectrometers such as the Nested Neutron Spectrometer (NNS) can be used to measure neutron fluence spectra but the raw measured data must be deconvolved (unfolded) with the detector’s response functions. The iterative Maximum-Likelihood Expectation–Maximization (MLEM) algorithm can be used to unfold the raw data, however it lacks an objective stopping criterion and produces an increasingly noisy solution as it iterates. In this work, we describe an objective stopping criterion that terminates MLEM unfolding of secondary neutron spectra in radiation therapy after solution convergence but prior to significant accumulation of noise. We validated the robustness of our stopping criterion by using it to unfold NNS measurements spanning a wide range of neutron fluence rates that were acquired around two linacs. We found that these unfolded spectra demonstrate a high level of agreement with the corresponding ideal unfolded spectra (obtained using Monte Carlo simulated spectra) and are relatively free of noise. Thus, use of our stopping criterion increases confidence in experimentally unfolded neutron spectra and can aid in improving carcinogenic risk estimates for patients receiving radiation therapy.