A modular electrical connector with separately shielded signal conductor pairs. In some embodiments, the connector is may be assembled from modules, each containing a pair of signal conductors with surrounding partially or fully conductive material. In some embodiments, the modules may have projecting portions, of conductive and/or dielectric material, that are shaped and positioned to reduce changes in impedance along the signal paths as a function of separation of conductive elements, when the connectors are separated by less than the functional mating range.