The interaction of radiation with matter can cause activation or fission reactions producing unstable residuals that decay with the emission of delayed-neutron and/or delayed-gamma radiation. This delayed radiation can be exploited for a variety of purposes, including homeland security, health physics, instrumentation and equipment design, and nuclear forensics. Here we report on capability that has been developed to provide automated simulations of delayed-neutron and/or delayed-gamma radiation using MCNP6. We present new high-fidelity delayed-gamma simulation results for models based on the neutron-fission experiments conducted by Beddingfield and Cecil to illustrate and validate this powerful feature.