A method and apparatus for ramping current in an electromagnet in which a coil is used to generate the magnetic field provides rapid changes in the generated magnetic field. The method allows a change in current in the coil to be accomplished more rapidly than by applying a step change in voltage, when superconducting coils subject to quenching are used or when nonsuperconducting coils subject to other physical limitations are used. The method requires that both the current I(t) through the coil and the first derivative of the current vary with respect to time t during the ramping period, so that magnitude of the derivative of the current is higher when the magnitude of applied current is lower, lower when the magnitude of the applied current is higher. One variation of this method supplies (or removes) a constant amount of power from the magnetic field of the magnet, while another variation compensates for both self-generated eddy current losses and self-generated high field effects. The method can be used to guide a magnetic seed and in other applications. The apparatus includes, in its most general form, an electromagnetic coil, a generator for applying an initial current to the coil, and a processor controlling the generator that causes the current to ramp from an initial to a final value in accordance with the methods described above.