Nuclear magnetic resonance (NMR) experiments at fields up to 58 T in pulsed magnets at the Dresden High Magnetic Field Laboratory are reported. The challenge to resolve NMR shifts in these time-dependent fields is addressed for the first time, and it is shown that this can indeed be accomplished with high precision with an internal reference. As a result, signal averaging is possible during a single magnetic field pulse, but also for multiple pulses. Thus, even very weak signals can in principle be recorded and their shifts can be determined. In a second set of experiments, the measurement of nuclear relaxation is investigated. Using adiabatic inversion with the inherent time dependence of the magnetic field and small-angle inspection, it is shown that relaxation measurements are possible, as well. The shift experiments were performed with ²⁷Al NMR on a mixture of aluminum metal and a Linde type A zeolite. For the relaxation studies, ²⁷Al NMR and ⁶⁹Ga NMR on the metals aluminum and gallium were preformed, respectively.