Recent interest in the dynamics of stratified turbulence has led to the development of newmodels for quantifying vertical transport of momentum and buoyancy (Chini et al 2022, Shah et al 2024). These models are still incomplete as they do not yet include all the relevant dynamics often present in real physical settings such as rotation and magnetic fields. Here we expand on prior work by adding rotation. Variation of the Rossby number affects the mean flow and perturbation dynamics independently. We conduct 3D direct numerical simulations of rotating, stochastically forced, strongly stratified turbulence (F r ≪ 1), and vary the Rossby number. We find that rotation gradually suppresses small-scale dynamics and, therefore, inhibits vertical transport as Ro decreases towards F r. The effect is particularly pronounced within the cores of emergent cyclonic vortices. For sufficiently strong rotation, vertical motions are suppressed.