Electromagnetic levitation of a liquid metal droplet is of great interest to study gas-liquid metal reactions. An important prerequisite for the evaluation of the overall mass transfer between the gas and metal is to characterize the geometry of the deforming molten droplet, which determines the interfacial reaction area. In this article, the free surface shape and dynamics of a molten 80%Ni-20%Cr droplet is investigated both experimentally and numerically. The frequencies associated to the oscillatory translational motions of the drop and to the vibrations of its free surface are measured using high-speed video image analysis. A 2D transient model is then presented, in which three interacting phenomena are considered: electromagnetic phenomena, the turbulent flow of liquid metal in the drop and the change in the drop shape. The numerical results presented demonstrate the capabilities of the model.