A magnetic device for gripping and clamping a workpiece in a machining unit or on a machining line including a magnetic plate having a distribution of high-energy permanent-magnet modules, which can be electrically activated. An auxiliary workpiece-holder plate made of ferromagnetic material rests on a main surface of the magnetic plate and has a top surface shaped in a way complementary to a surface of the workpiece that rests thereon. The workpiece rests on the top surface of the auxiliary workpiece-holder plate only in points corresponding to some supporting pads, while the facing surfaces of the workpiece and auxiliary workpiece-holder plate are kept slightly set apart from one another for most of their extension.