Electrical connection system comprising a primary connection device and a secondary connection device, the primary connection device comprising a shielded cap and primary conductive contacts which extend at least partially inside the shielded cap, the secondary connection device comprising a secondary electrical board which has a secondary mass surface, secondary conductive contacts which extend from an installation surface of the secondary electrical board which is surrounded by the secondary mass surface, and a resilient conductive material which is attached to the secondary mass surface, the electrical connection system being arranged so that the primary conductive contacts are electrically connected to the secondary electrical contacts inside the shielded cap and the shielded cap extends on the resilient conductive material by compressing it.