Calculated estimates of neutron doses received by atomic-bomb survivors at Hiroshima and Nagasaki have not included contributions from delayed neutrons emitted by fission products in the debris cloud, although the possibility of a significant contribution from this source has been suggested. In the present work, an established model accounting for gamma-ray kermas from these fission products is adapted to provide the desired neutron kerma estimates. Adaptations include use of explicit time dependence of neutron emitters, properly folded with the time-dependent phenomenology of the explosion itself, and detailed air-over-ground neutron transport with a source having an energy spectrum characteristic of these delayed neutrons. Results show that delayed neutrons are indeed negligible contributors to atomic-bomb survivor dosimetry, as well as to neutron activations at Hiroshima. About half the activation at Nagasaki, however, is due to the delayed component. Calculated activation of cobalt, a revision of previous estimates, is compared to measured values at Hiroshima and at Nagasaki. The causes of the substantial discrepancies are discussed and compared to previously reported discrepancies for sulfur activation. Additional investigation is recommended.