Potential energy curves and radial couplings have been calculated for electron capture from H by the ground and metastable excited states of Ne²⁺. The electron transfer can be accompanied by excitation of a core electron of Ne²⁺. Cross sections and rate coefficients have been estimated at collision energies of a few eV. The fastest rate coefficient for electron capture, 6*10^-11 cm³ s^-1, is that from the ¹D entrance channel. This rate is much too low to explain values inferred from observations of planetary nebulae.