A shielded electrical cable is disclosed that includes a plurality of spaced apart conductor sets where each conductor set includes one or more insulated conductors. The cable further includes first and second shielding films that include concentric portions, pinched portions, and transition portions arranged such that the concentric portions are substantially concentric with one or more end conductors of each conductor set, the pinched portions form pinched portions of the cable on two sides of the conductor set, and the transition portions provide gradual transitions between the concentric portions and the pinched portions. The cross-sectional areas of the transition portions are less than the cross-sectional areas of the conductors. The radius of curvature of the shielding films in the transverse direction is at least 100 microns.