Recently, several Lagrangian microphysical models have been developed which use a large number of (computational) particles to represent a cloud. In particular, the collision process leading to coalescence of cloud droplets or aggregation of ice crystals is implemented differently in various models. Three existing implementations are reviewed and extended, and their performance is evaluated by a comparison with well-established analytical and bin model solutions. In this first step of rigorous evaluation, box model simulations, with collection/aggregation being the only process considered, have been performed for the three well-known kernels of Golovin, Long and Hall. <br><br> Besides numerical parameters, like the time step and the number of simulation particles (SIPs) used, the details of how the initial SIP ensemble is created from a prescribed analytically defined size distribution is crucial for the performance of the algorithms. Using a constant weight technique, as done in previous studies, greatly underestimates the quality of the algorithms. Using better initialisation techniques considerably reduces the number of required SIPs to obtain realistic results. From the box model results, recommendations for the collection/aggregation implementation in higher dimensional model setups are derived. Suitable algorithms are equally relevant to treating the warm rain process and aggregation in cirrus.