Ocean volume and tracer transports are commonly computed on density surfaces because doing so approximates the semi-Lagrangian mean advective transport. The resulting density-averaged transport can be related approximately to Eulerian-averaged quantities via the Temporal Residual Mean (TRM), valid in the limit of small isopycnal height fluctuations. This article builds on a formulation of the TRM for volume fluxes within Neutral Density surfaces, (the “NDTRM”), selected because Neutral Density surfaces are constructed to be as neutral as possible while still forming well-defined surfaces. This article derives a TRM, referred to as the “Neutral TRM” (NTRM), that approximates volume fluxes within surfaces whose vertical fluctuations are defined directly by the neutral relation. The purpose of the NTRM is to more closely approximate the semi-Lagrangian mean transport than the NDTRM, because the latter introduces errors associated with differences between the instantaneous state of the modeled/observed ocean and the reference climatology used to assign the Neutral Density variable. It is shown that the NDTRM collapses to the NTRM in the limiting case of a Neutral Density variable defined with reference to the Eulerian-mean salinity, potential temperature and pressure, rather than an external reference climatology, and therefore that the NTRM approximately advects this density variable. This prediction is verified directly using output from an idealized eddy-resolving numerical model. The NTRM therefore offers an efficient and accurate estimate of modeled semi-Lagrangian mean transports without reference to an external reference climatology, but requires that a Neutral Density variable be computed once from the model’s time-mean state in order to estimate isopycnal and diapycnal components of the transport.