We propose a new passive shimming strategy for variable-field NMR experiments, in which the magnetic field produced by paramagnetic shim pieces placed inside the magnet bore compensates the inhomogeneity of a variable-field magnet for a wide range of magnet currents. Paramagnetic shimming is demonstrated in Li-7, Rb-87, and Sc-45 NMR of a liquid solution sample in magnetic fields of 3.4, 4.0, and 5.4 T at a fixed carrier frequency of 56.0 MHz. Since both the main-field inhomogeneity and the paramagnetic magnetization are proportional to the main-magnet current, the resonance lines are equally narrowed by the improved field homogeneity with an identical configuration of the paramagnetic shim pieces. Paramagnetic shimming presented in this work opens the possibility of high-resolution variable-field NMR experiments. (C) 2014 Elsevier Inc. All rights reserved.