A method of riveting includes drilling a hole in a workpiece with a drill bit held in a spindle mounted on an axial centerline of a drill/rivet machine. The drill descends through a drill/suction cavity of a movable shuttle and drill chips cut by the drill bit are suctioned away from the workpiece as they are made. The drill bit is withdrawn to a level just above the drill/suction cavity, which is then moved to position a rivet insert station over the newly drilled hole in the workpiece. A rivet is blown into the rivet insert station, is guided into alignment with the hole and injected directly into the hole by air pressure. The shuttle moves a rivet die over the newly installed rivet in the hole and a driver of an electromagnetic riveter is lowered into contact with the die, which in turn is pressed against the rivet head. Another rivet die is pressed against the rivet tail on the other side of the panel by a driver of another electromagnetic riveter. Both electromagnetic actuators are energized to propel the drivers toward each other and cause the dies to upset the rivet.