The Second Target Station project at Oak Ridge National Laboratory will develop a cold neutron source to meet growing experimental needs. This paper describes calculations of the residual dose rates associated with the monolith shield plug and the beamline bunker, two key conventional operations and radiation safety features. While neutron production is active, the instrument hall outside the bunker must be generally accessible with dose rates of less than 0.25 mrem/h. When neutron production is halted, the bunker must be accessible for hands-on maintenance operations. These two requirements form the cause for the assessments reported herein of residual dose rates caused by the monolith shield plug and residual dose rates in the bunker. The monolith shield plug was shown to not produce significant dose rates inside the bunker after a 20-year lifetime, and the residual dose rates inside the bunker for the case of an operating beamline were shown to reasonably allow for hands-on maintenance. These calculations are based on preliminary design models of the relevant systems. Additionally, an example showing the significance of considering neutron supermirror physics in transport calculations that track nuclide production and destruction rates to produce gamma sources for residual dose rate calculations is included. The example shows that if neutron supermirror physics is not considered, dose rate fields may be significantly underpredicted.