The Glazier-Graner-Hogeweg (GGH) model is a cellular automata framework for representing the time evolution of cellular systems, appealing because unlike many other individual-cell-based models it dynamically simulates changes in cell shape and size. Proliferation has seen some implementation into this modelling framework, but without consensus in the literature as to how this behaviour is best represented. Additionally, the majority of published GGH model implementations which feature proliferation do so in order to simulate a certain biological situation where mitosis is important, but without analysis of how these proliferation routines operate on a fundamental level. Here, a method of proliferation for the GGH model which uses separate cell phenotypes to differentiate cells which have entered or just left the mitotic phase of the cell cycle is presented and demonstrated to correctly predict logistic growth on a macroscopic scale (in accordance with experimental evidence). Comparisons between model simulations and the generalised logistic growth model provide an interpretation of the latter's 'shape parameter', and the proliferation routine used here is shown to offer the modeller somewhat predictable control over the proliferation rate, important for ensuring temporal consistency between different cellular behaviours in the model. All results are found to be insensitive to the inclusion of active cell motility. The implications of these simulated proliferation assays towards problems in cell biology are also discussed.