The melting curve of neon is determined from nonequilibrium molecular dynamics simulations performed at constant pressure, using ab initio pair potentials. The effects of various approximations on the predicted melting points are investigated through the use of pair potentials calculated at different levels of accuracy, and the inclusion of quantum effects on the motion via a Wigner-Kirkwood quantum effective potential. To avoid superheating of the model crystal, nucleation sites for melting are provided by creating clusters of void defects in the crystal prior to heating. The calculated melting curves are shown to be in good agreement with experimental measurements. Comparisons are made with similar calculations previously carried out for argon.