A Monte Carlo exchange technique is used to study segregation in thin ceramic films with application to MgO/MnO. The approach is not restricted to the dilute limit. Surface concentrations as a function of temperature and film composition are determined directly from the simulations. For all compositions studied (Mn chi Mg1-chi O, 0 <= chi <= 1) the (001) surface is Mn2+ rich; the occupancy of sites by Mn2+ decreases rapidly with depth. The ratio of the number of Mn2+ to Mg2+ ions at the surface decreases as a function of temperature. The calculated enthalpies of segregation of Mn2+ for the thin film are strongly dependent on the total Mn2+ concentration at small Mn2+ concentrations, with the enthalpy of segregation varying by a factor of two with surface coverage.