An electromechanical brake calliper, comprising a calliper body and an electromechanical actuator including: - a screw, rotatable about a longitudinal axis (x); - a nut screw, rotationally coupled to said screw, the nut screw being movable along a direction parallel to the longitudinal axis (x) of the screw; - a movable thrust element (18, 32), comprising its own longitudinal axis (y) and axially juxtaposed to the nut screw, onto which movable thrust element (18, 32) said nut screw engages; - a coupling interface between the nut screw and the movable thrust element (18, 32), comprising at least a first coupling surface, obtained in the nut screw, and at least a second coupling surface (C', C IV), obtained in the movable thrust element (18, 32), said second surface (C', C IV) being at least in part coupled to the first surface and cooperating in a thrust relation with said first surface; wherein one of said coupling surfaces (C, C', C IV) is concave and the other (C', C IV) of said surfaces is convex, and engages the concave coupling surface, the arrangement of said surfaces (C, C', C IV) being such that it allows a relative oscillation of the nut screw with respect to the movable thrust element (18, 32) about a single predetermined axis (k), essentially transversal to the longitudinal axis (x) of the screw; and wherein the relative rotation about the longitudinal axis (y) between the nut screw and the piston is hindered; said actuator being characterised in that: the first and the second coupling surfaces (C, C', C IV) are portions of coaxial cylindrical surfaces, substantially complementary to one another, the nut screw and the movable thrust element (18, 32) being shaped so as to allow a relative oscillation thereof about the axis common to said first and second coupling surfaces (C, C', CIV). - a screw, rotatable about a longitudinal axis (x); - a nut screw, rotationally coupled to said screw, the nut screw being movable along a direction parallel to the longitudinal axis (x) of the screw; - a movable thrust element (18, 32), comprising its own longitudinal axis (y) and axially juxtaposed to the nut screw, onto which movable thrust element (18, 32) said nut screw engages; - a coupling interface between the nut screw and the movable thrust element (18, 32), comprising at least a first coupling surface, obtained in the nut screw, and at least a second coupling surface (C', C IV), obtained in the movable thrust element (18, 32), said second surface (C', C IV) being at least in part coupled to the first surface and cooperating in a thrust relation with said first surface; wherein one of said coupling surfaces (C, C', C IV) is concave and the other (C', C IV) of said surfaces is convex, and engages the concave coupling surface, the arrangement of said surfaces (C, C', C IV) being such that it allows a relative oscillation of the nut screw with respect to the movable thrust element (18, 32) about a single predetermined axis (k), essentially transversal to the longitudinal axis (x) of the screw; and wherein the relative rotation about the longitudinal axis (y) between the nut screw and the piston is hindered; said actuator being characterised in that: the first and the second coupling surfaces (C, C', C IV) are portions of coaxial cylindrical surfaces, substantially complementary to one another, the nut screw and the movable thrust element (18, 32) being shaped so as to allow a relative oscillation thereof about the axis common to said first and second coupling surfaces (C, C', CIV).