In many industrial processes dealing with liquid metals or semiconductors, the quality of the resulting product is directly affected by the flow of the melt. These melts are often too hot or too aggressive for direct flow measurement with conventional techniques. One candidate for a feasible application to metallurgical processes is the contactless inductive flow tomography (CIFT), which works by exposing the melt to a magnetic excitation field, measuring the flow-induced perturbances to that field and solving the underlying inverse problem. This paper gives an overview about the theory of CIFT and its application in small-scale models of continuous casting under the influence of a strong static magnetic field.