Pulsed magnets generate the highest magnetic fields as brief transients during which the observation of NMR is difficult, however, this is the only route to unique insight into material properties up to the regime of 100 T. Here, it is shown how rather broad NMR spectra can be assembled in a pulsed magnet during a single field pulse by using the inherent time dependence of the field for the recording of field-stepped free induction decays that cover a broad frequency range. The technique is then applied to 11B NMR of the spin-dimer system SrCu₂(BO₃)₂, a magnetic insulator known to undergo a series of field-driven changes of the magnetic ground state. At peak fields of about 54T at the Dresden High Magnetic Field Laboratory, 11B NMR spectra spanning a total of about 9MHz width are reconstructed. The results are in good accordance with a change from a high-temperature paramagnetic state to a low-temperature commensurate superstructure of field-induced spin-dimer triplets.