Metre-scale cycles in ancient peritidal carbonate facies have long been thought to represent the product of shallow water carbonate accumulation under orbitally controlled sea level oscillations. The theory remains somewhat controversial, however, and a contrasting view is that these cycles are the product of intrinsic, and perhaps random, processes. Owing to this debate, it is important to understand the conditions that do, or do not, favour the preservation of orbital forcing, and the precise stratigraphical expression of that forcing. In this work, a one-dimensional forward model of carbonate accumulation is used to test the ability of orbitally paced sea level changes to reconstruct cyclicities and cycle stacking patterns observed in greenhouse peritidal carbonate successions. Importantly, the modelling specifically tests insolation-based sea level curves that likely best reflect the pattern and amplitude of sea level change in the absence of large-scale glacioeustasy. We find that such sea level histories can generate precession and eccentricity water depth/facies cycles in our models, as well as eccentricity-modulated cycles in precession cycle thicknesses (bundles). Nevertheless, preservation of orbital forcing is highly sensitive to carbonate production rates and amplitudes of sea level change, and the conditions best suited to preserving orbital cycles in facies/water depth are different to those best suited to preserving eccentricity-scale bundling. In addition, it can be demonstrated that the preservation of orbital forcing is commonly associated with both stratigraphic incompleteness (missing cycles) and complex cycle thickness distributions (e.g. exponential), with corresponding implications for the use of peritidal carbonate successions to build accurate astronomical timescales.