We have investigated the differential capacitance between two stacked, circular quantum dots. An expression defining such differential capacitance has been derived on the basis of that for the self-capacitance of a single quantum dot. By means of a self-consistent simulation we have obtained numerical results showing that the differential capacitance between the two dots is strongly influenced by shell-filling effects, and that the classical limit of the parallel-plate capacitor is retrieved when the two dots are in close proximity. Our results represent a contribution to the effort for the definition of a capacitance matrix for a complex system of quantum dots. (C) 1997 Elsevier Science B.V. All rights reserved.