An anchor socket system for vertically supporting a post includes external and internal, open-ended cylinders, wherein the external cylinder includes first and second semi-cylinder halves each having mirroring tapers and semi-annular upper rims on each respective inner facing wall. Tightening bolts in communication with the internal and external cylinders are rotated to raise the internal cylinder relative to the external cylinder, thereby causing tapered wedges on the outer facing surface of the internal cylinder to exert pressure against the corresponding tapers on the inner facing surface of the external cylinder. As the diameter of the internal cylinder contracts, pressure is exerted against a post by the inner facing walls of the internal cylinder while the outer facing walls of the external cylinder halves simultaneously exert pressure against the inner facing surface of a core-drilled hole, thereby locking the anchor socket and post into place within the core-drilled hole.