The Monte Carlo method is used to explicitly show that solid-fluid phase boundaries determined by the visual appearance and disappearance of a solidlike structure is quite different from that expected in the bulk system and predicted by a full free-energy analysis. This feature of the computer simulations is almost self-evident and may be understood by the argument that the phase coexistence in the finite system is inevitably suppressed by the non-negligible interfacial energy compared with that in the infinite (bulk) system. One of the discrepancies among the recent simulation studies for the high-temperature phase behavior of a model C-60 is found to be the consequence of overlooking the above feature of computer simulations.