Tools based on optimal transport are widely applicable to signal-processing problems common in chemical analysis. Our work shows that these methods can also benefit the monitoring of chemical reactions by NMR spectroscopy. We present how the program Magnetstein, based on the optimal transport Wasserstein metric, allows for efficient determination of reaction kinetics. Contrary to conventional approaches, the method works well even for spectra with significant peak overlap and non-standard line shapes caused, for example, by magnetic field inhomogeneity. The method has only two parameters, which can be set to constant values for many data sets.