A cable header connector includes a contact module having a support body and a plurality of cable assemblies held by the support body and arranged in a column. The cable assemblies each have a contact terminated to a cable and a ground shield coupled to and providing electrical shielding for the contact sub-assembly. The support body has contact channels extending along respective contact channel axes which are parallel to each other, and at least one cable channel intersecting the contact channels. The cables extend through the contact channels and through the at least one cable channel to an outside of the support body. The cables emerging from the support body at corresponding cable exits at respective angles to the contact channel axes.