The stability of an interface between a liquid metal and an insulating atmosphere, in which an inductor generates a uniform alternating magnetic field, is investigated, with particular attention given to the influence of the electrical conductivity of the liquid. In a range of high frequencies, a quasi-steady approximation is justified, in which the pulsation of the electromagnetic forces is negligible compared with their mean part, and the unsteadiness of the magnetic field only appears through the skin effect. By means of a linear analysis, the influence of the alternating magnetic field on a perturbation of the interface is found to be neutral for wavevectors perpendicular to the magnetic field, and stabilizing for any other orientation. The stabilizing effect is largest when the angle between the wavevector and the magnetic field is zero, and it increases with increasing wavenumber. This effect, maximum for an infinitely conducting medium, quickly decreases with the electrical conductivity.