A connector for microelectronic elements includes a sheetlike dielectric layer having a plurality of through holes desirably arranged in a rectangular grid pattern. Each hole is provided on one major surface with a generally laminar contact having at least one projection extending inwardly over the through hole. Contact pads on the second major surface of the dielectric layer overlie the through holes to provide a blind end which is electrically connected to the other contact by means of a metal layer lining the through hole. The resulting connectors provide low or zero insertion force sockets for mounting microelectronic elements having bump leads thereto. The bump leads may be received within corresponding sockets without engagement with the contact or projection, and then, by movement in a lateral direction, engaging the contact or projection to provide electrical connection to the socket. The dielectric layer may be formed from flexible and/or compressible materials, such as polyimide, whereby deflection of the connector will cause the top contacts surrounding the through hole to move radially inward into engagement with the bump leads on the microelectronic element.