‘Cell-based’ models provide a powerful computational tool for studying the mechanisms underlying the growth and dynamics of biological tissues in health and disease. An increasing amount of quantitative data with cellular resolution has paved the way for the quantitative parameterisation and validation of such models. However, the numerical implementation of cell-based models remains challenging, and little work has been done to understand to what extent implementation choices may influence model predictions. Here, we consider the numerical implementation of a popular class of cell-based models called vertex models, used extensively to simulate epithelial tissues. In two-dimensional vertex models, a tissue is approximated as a tessellation of polygons and the vertices of these polygons move due to mechanical forces originating from the cells. We analyse how the model predictions may be affected by implementation-specific parameters, such as the size of the numerical time step. We find that vertex positions and summary statistics are sensitive to multiple implementation parameters. For example, the predicted tissue size decreases with decreasing cell cycle durations, and cell rearrangement may be suppressed by large time steps. These findings are counter-intuitive and illustrate that model predictions need to be thoroughly analysed and implementation details carefully considered when applying cell-based computational models in a quantitative setting.