We have performed large-scale molecular dynamics simulations of coexisting solid and liquid phases using 4epsilon(sigma/r)(n) interactions for n=9 and n=12, and for Lennard-Jones systems, in order to calculate the equilibrium melting curve. The coexisting systems evolve rapidly toward the melting temperature. The P-T melting curves agree well with previous calculations, as do the other bulk phase properties. The melting curve for the Lennard-Jones system, evaluated using various truncations of the potential, converges rapidly as a function of the potential cutoff, indicating that long-range corrections to the free energies of the solid and liquid phases very nearly cancel. This approach provides an alternative to traditional methods of calculating melting curves.