Herein, the annealing of highly polar (S)-(−)-4-methoxymethyl-1,3-dioxolan-2one (S-methoxy-PC) within alumina and silica porous membranes characterized by different pore diameters was studied by means of dielectric spectroscopy. We found a significant slowing down of the structural dynamics of confined S-methoxy-PC with annealing time below and, surprisingly, also above the glass transition temperatures of the interfacial layer, T g,interfacial . Furthermore, unexpectedly, a change in the slope of temperature dependencies of the characteristic time scale of this process τ anneal , at T g,interfacial for all confined samples, was reported. By modeling τ anneal (T), we noted that the observed enormous variation of τ anneal results from a decrease of the pore radius due to the vitrification of the interfacial molecules. This indicates that the enhanced dynamics of confined materials upon cooling is mainly controlled by the interfacial molecules.