A novel zero insertion (and removal) force multi-pin coaxial connector for providing connections via controlled impedance paths is formed using a conductive elastomer as a frame (8) which forms the shield of a plurality of coaxial connectors and a plurality of circular openings formed in the conductive elastomer frame, each said opening corresponding to a single coaxial connection. An annular insulating ring (5), which forms the dielectric of an associated one of the coaxial connectors, is located in each annular opening of the conductive elastomer frame and an elastomer through-conductive member (6) which forms the center conductor of its associated coaxial connector is located within the circular opening of each insulating ring. In this manner, the conductive elastomer frame forms the shield of a plurality of coaxial connectors. A connector board for use with a plurality of coaxial cables is designed such that it will properly mate with the conductive elastomer frame and conductive elastomer through-conductive members, thus connecting the plurality of coaxial cables to one side of their associated coaxial connectors within the conductive elastomer frame. The connector board contains a plurality of conductive paths which are formed so as to properly abut the conductive elastomer frame and the elastomer through-conductive members of the coaxial connector. In this manner, each coaxial cable is connected through the zero insertion force multi-pin connector to their associated conductive paths on the printed circuit board. Alternatively, the multi-pin connector is used to connect two printed circuit boards.