In a contact connecting of preferably a number of shielded conductor pairs to a board in particular of a plug for high-speed data connections, the board is formed of multiple layers and contains a conductor path tier and a ground tier. A ground contact zone of the ground tier projects, in a tongue-like manner, towards the connected conductor pairs. In the region of the ground contact zone, the individual conductor pairs are pressed in contact against the corresponding pair shielding thereof. To this end, in particular a clamping element is provided that is also used to achieve the shield contacting.