Abstract: We have studied the supercooling and superheating of Al and Zn in the temperature range between 0.5 and 1.2 K. The samples, collections of dispersed and isolated small spheres, were prepared by spraying of the molten metal into liquid nitrogen. The supercooling and superheating fields obtained are, by all indications, close to the theoretical limit. From the supercooling fields observed we determined the Ginzburg-Landau parameter κ(Tc) = 0.015, for both Al and Zn. The superheating field exhibits a strong temperature dependence near Tc, which reflects the extremely non-local electrodynamics of the materials. The results are discussed in the light of recent theoretical work.