Coarsening of surfactant-stabilized oil-in-water emulsions (C12E5-decane-D2O) induced by a fast temperature drop from their microemulsion phase is studied by H-1 stimulated-echo-type pulsed-field-gradient spin-echo (PGSE) NMR spectroscopy. The data obtained on a small amount of hexamethyldisilane dissolved in the oil phase display two distinct diffusion coefficients. The slower diffusion is interpreted in terms of large droplets containing the oil that had been expelled from the original microemulsion droplets. The faster diffusion belongs to smaller microemulsion droplets that coexist with the large oil droplets. The results show that the investigated emulsions exhibit regular Ostwald ripening. Both the actual amounts of the expelled oil and the obtained coarsening rates agree well with theoretical estimates. As a consequence of fast surfactant exchange among the different droplets, the diffusion of the surfactant molecules is described by a single diffusion coefficient.