Methods of measuring the displacement and velocity of the surfaces of metal objects under the action of a pulsed magnetic field are considered: using an interferometer, fiber-optic Bragg gratings and by the magnitude of the displacement of the image of the edge of the object. Estimates of the possible range of measurement of displacement and velocity by various methods are presented, in particular, examples of current waveforms, fluctuations in the intensity of the interference pattern, spectral characteristics of the laser emitter and the Bragg gratings used are given. Recommendations on the use of the methods for registering high-speed displacements in various loading schemes initiated by a pulsed magnetic field of microsecond duration with an induction amplitude of up to 40 T are given.