A board-to-board connector for connecting printed boards (2, 3) to each other, the connector comprising: a receptacle comprising a plurality of signal contact elements to be electrically connected to one of the printed boards, and a plug comprising a plurality of signal contact elements to be electrically connected to the other of the printed boards, the signal contact elements (12, 22) being configured so that each of the signal contact elements of the plug is in contact with the corresponding signal contact element of the receptacle when the plug has been inserted into the receptacle, wherein the receptacle comprises an electromagnetic interference shield which continuously or discontinuously surrounds the plurality of signal contact elements of the receptacle, and the plug comprises an electromagnetic interference shield which continuously or discontinuously surrounds the plurality of signal contact elements of the plug, and wherein the shield of the receptacle and the shield of the plug are configured to be in direct contact with each other when the plug has been inserted into the receptacle, the contact arrangement of the shields (13, 23) being provided along the entire perimeter of the connector, wherein the shield of the plug is provided with a plurality of first abutment portions for bringing the shield of the plug into direct contact with the shield of the receptacle, the first abutment portions being positioned at intervals around the entire shield of the plug, wherein the shield of the receptacle is provided with a plurality of second abutment portions for bringing the shield of the receptacle into direct contact with the shield of the plug, the second abutment portions being positioned at intervals around the entire shield of the receptacle characterized in that the first and second abutment portions (134, 232) are positioned so that the first abutment portions are arranged alternately with the second abutment portions when the plug has been inserted into the receptacle. a receptacle comprising a plurality of signal contact elements to be electrically connected to one of the printed boards, and a plug comprising a plurality of signal contact elements to be electrically connected to the other of the printed boards, the signal contact elements (12, 22) being configured so that each of the signal contact elements of the plug is in contact with the corresponding signal contact element of the receptacle when the plug has been inserted into the receptacle, wherein the receptacle comprises an electromagnetic interference shield which continuously or discontinuously surrounds the plurality of signal contact elements of the receptacle, and the plug comprises an electromagnetic interference shield which continuously or discontinuously surrounds the plurality of signal contact elements of the plug, and wherein the shield of the receptacle and the shield of the plug are configured to be in direct contact with each other when the plug has been inserted into the receptacle, the contact arrangement of the shields (13, 23) being provided along the entire perimeter of the connector, wherein the shield of the plug is provided with a plurality of first abutment portions for bringing the shield of the plug into direct contact with the shield of the receptacle, the first abutment portions being positioned at intervals around the entire shield of the plug, wherein the shield of the receptacle is provided with a plurality of second abutment portions for bringing the shield of the receptacle into direct contact with the shield of the plug, the second abutment portions being positioned at intervals around the entire shield of the receptacle characterized in that the first and second abutment portions (134, 232) are positioned so that the first abutment portions are arranged alternately with the second abutment portions when the plug has been inserted into the receptacle.