An electrical connector for high speed signals. The connector has multiple conductive elements that may serve as signal or ground conductors. A member formed with lossy material and conductive compliant members may be inserted in the connector. The conductive compliant members may be aligned with conductive elements of the connector configured as ground conductors. For a connector configured to carry differential signals, the ground conductors may separate pairs of signal conductors. The member may further include a conductive web, embedded within the lossy material, that interconnects the conductive compliant members. For a receptacle connector, the conductive elements may have mating contact portions aligned along opposing surfaces of a cavity. The conductive elements may have contact tails for attachment to a printed circuit board and intermediate portions connecting the mating contact portions and the contact tails. The conductive compliant members may press against the intermediate portions.