A three-dimensional, Potts model of liquid phase sintering in a system with full solid wetting was introduced in order to investigate the coarsening kinetics and microstructures associated with this process. Kinetic Monte Carlo simulation was used to probe the coarsening dynamics and obtain the properties of solid particles, including the volume of critical nuclei and the distribution of particle sizes as a function of time. It was found that the average particle volume increased linearly with time and that the particle size distributions were consistent with those obtained experimentally, as in the W-Ni-Fe and Sn-Pb systems. In obtaining these results careful consideration was given to the role of the initial microstructural features in the subsequent evolution of the system.