A metascreen designed to achieve near-field subwavelength focusing at a given frequency is shown to operate as a superdirective antenna in the vicinity of that frequency at the far field. A metascreen for microwave frequencies based on a simple perfect electrically conducting screen is initially used to explain the principle of operation as a superdirective antenna and to distinguish this operation mode from that resulting in near-field subwavelength focusing. A similar metascreen design based on a silver screen of a finite thickness is then used to demonstrate superdirectivity with nanoantennas in the optical frequency regime.