A modular electrical connector with separately shielded signal conductor pairs. The connector may be assembled from modules, each containing a pair of signal conductors with surrounding partially or fully conductive material. Modules of different sizes may be assembled into wafers, which are then assembled into a connector. Wafers may include lossy material. In some embodiments, shielding members of two mating connectors may each have compliant members along their distal portions, such that, the shielding members engage at points of contact at multiple locations, some of which are adjacent the mating edge of each of the mating shielding members.