In this work we implement approximate Bayesian computational methods to improve the design of a wound-healing assay used to quantify cell-cell interactions. This is important as cell-cell interactions, such as adhesion and repulsion, have been shown to play an important role in cell migration. Initially, we demonstrate with a model of an ideal experiment that we are able to identify model parameters for agent motility and adhesion, given we choose appropriate summary statistics. Following this, we replace our model of an ideal experiment with a model representative of a practically realisable experiment. We demonstrate that, given the current (and commonly used) experimental set-up, model parameters cannot be accurately identified using approximate Bayesian computation methods. We compare new experimental designs through simulation, and show more accurate identification of model parameters is possible by expanding the size of the domain upon which the experiment is performed, as opposed to increasing the number of experimental repeats. The results presented in this work therefore describe time and cost-saving alterations for a commonly performed experiment for identifying cell motility parameters. Moreover, the results presented in this work will be of interest to those concerned with performing experiments that allow for the accurate identification of parameters governing cell migratory processes, especially cell migratory processes in which cell-cell adhesion or repulsion are known to play a significant role.