Multi-millennial transient simulations of climate changes have a range of important applications, such as for investigating key geologic events and transitions for which high-resolution palaeoenvironmental proxy data are available, or for projecting the long-term impacts of future climate evolution on the performance of geological repositories for the disposal of radioactive wastes. However, due to the high computational requirements of current fully coupled general circulation models (GCMs), long-term simulations can generally only be performed with less complex models and/or at lower spatial resolution. In this study, we present novel long-term “continuous” projections of climate evolution based on the output from GCMs, via the use of a statistical emulator. The emulator is calibrated using ensembles of GCM simulations, which have varying orbital configurations and atmospheric CO2 concentrations and enables a variety of investigations of long-term climate change to be conducted, which would not be possible with other modelling techniques on the same temporal and spatial scales. To illustrate the potential applications, we apply the emulator to the late Pliocene (by modelling surface air temperature – SAT), comparing its results with palaeo-proxy data for a number of global sites, and to the next 200 kyr (thousand years) (by modelling SAT and precipitation). A range of CO2 scenarios are prescribed for each period. During the late Pliocene, we find that emulated SAT varies on an approximately precessional timescale, with evidence of increased obliquity response at times. A comparison of atmospheric CO2 concentration for this period, estimated using the proxy sea surface temperature (SST) data from different sites and emulator results, finds that relatively similar CO2 concentrations are estimated based on sites at lower latitudes, whereas higher-latitude sites show larger discrepancies. In our second illustrative application, spanning the next 200 kyr into the future, we find that SAT oscillations appear to be primarily influenced by obliquity for the first 120 kyr, whilst eccentricity is relatively low, after which precession plays a more dominant role. Conversely, variations in precipitation over the entire period demonstrate a strong precessional signal. Overall, we find that the emulator provides a useful and powerful tool for rapidly simulating the long-term evolution of climate, both past and future, due to its relatively high spatial resolution and relatively low computational cost. However, there are uncertainties associated with the approach used, including the inability of the emulator to capture deviations from a quasi-stationary response to the forcing, such as transient adjustments of the deep-ocean temperature and circulation, in addition to its limited range of fixed ice sheet configurations and its requirement for prescribed atmospheric CO2 concentrations.