A modular electrical connector with broad-side coupled signal conductors in a right angle intermediate portion and edge coupled end portions. Broadside coupling provides balanced pairs for very high frequency operation, while edge coupling provides a high density interconnection system at low cost. Each module has separately shielded signal conductor pairs. The shielding is shaped to avoid or suppress undesirable propagation modes within an enclosure formed by shielding per module. Lossy material is selectively placed within and outside the shielding per module to likewise avoid or suppress unwanted signal propagation.