Apparatus for clamping workpieces on machine tools, comprising: - at least one basic frame fixable to a machine tool (M) for machining a workpiece (P); - at least one clamping unit associated with said basic frame in a movable manner between a release position and a clamping position of said workpiece (P), passing through a plurality of intermediate transient positions; - at least one hydraulic actuator , provided with a fixed portion , associated with said basic frame , and a movable portion , connected to said clamping unit , said hydraulic actuator comprising at least a first chamber which can be supplied with a first pressurized hydraulic fluid to displace said clamping unit from said release position to said clamping position, said first chamber being connectable to a first sensing device for sensing the pressure of said first hydraulic fluid; characterized by the fact that: - said apparatus comprises at least one sensing channel formed on at least one of said basic frame and said clamping unit , which can be supplied with pressurized air and which is connectable to a sensing sensor for sensing the pressure of said air, wherein said sensing channel is hermetically sealed when said clamping unit is in the clamping position and is open outwards at least when said clamping unit is in said intermediate transient positions; and - said first sensing device and said sensing sensor are connectable to a control system adapted to authorize the machining of said workpiece (P) when the pressure of said first hydraulic fluid in said first chamber and the pressure of said air in said sensing channel are simultaneously higher than their respective threshold values. - at least one basic frame fixable to a machine tool (M) for machining a workpiece (P); - at least one clamping unit associated with said basic frame in a movable manner between a release position and a clamping position of said workpiece (P), passing through a plurality of intermediate transient positions; - at least one hydraulic actuator , provided with a fixed portion , associated with said basic frame , and a movable portion , connected to said clamping unit , said hydraulic actuator comprising at least a first chamber which can be supplied with a first pressurized hydraulic fluid to displace said clamping unit from said release position to said clamping position, said first chamber being connectable to a first sensing device for sensing the pressure of said first hydraulic fluid; - said apparatus comprises at least one sensing channel formed on at least one of said basic frame and said clamping unit , which can be supplied with pressurized air and which is connectable to a sensing sensor for sensing the pressure of said air, wherein said sensing channel is hermetically sealed when said clamping unit is in the clamping position and is open outwards at least when said clamping unit is in said intermediate transient positions; and - said first sensing device and said sensing sensor are connectable to a control system adapted to authorize the machining of said workpiece (P) when the pressure of said first hydraulic fluid in said first chamber and the pressure of said air in said sensing channel are simultaneously higher than their respective threshold values. <EOS>