The availability of a superconducting connection between adjacent niobium radio-frequency (RF) cavities with the capability to carry up to 30 mT of the magnetic flux would be particularly of great benefit to layouts of long accelerators like the International Linear Collider (ILC). It would shorten the distances between structures and therefore the total length of an accelerator with the associated cost reductions. In addition, the superconducting connection would be ideal for a superstructure-two multi-cell cavities connected through a half wavelength long beam pipe providing the coupling. Two single-cell niobium cavities have been designed with Nb-1Zr flanges welded to one of the irises to allow a connection between them with a niobium gasket. A transition to the normal-conducting state of the connection due to the applied RF field causes a reduction of the cavities' quality factor. The cavity design will be presented in this contribution along with possible choices of materials for the joint.