A method and apparatus for a positioning system for electromagnetic riveting. The apparatus comprises a plate and a biasing system physically associated with the plate. The plate is configured to be positioned relative to a first workpiece, and is further configured to electromagnetically engage an electromagnetic tool. The biasing system is configured to physically engage a second workpiece. The biasing system is further configured to hold the plate in a desired position relative to the first workpiece during a number of operations performed by the electromagnetic tool while the plate is electromagnetically engaged with the first workpiece.