Disclosed are embodiments of a pivot mount for an optical aiming device. The pivot mount can be attached to an accessory rail, such as a MIL-STD-1913 rail, extending along the top of a receiver or handguard of a firearm. The pivot mount allows an attached optical aiming device to be pivoted between a use position and a storage position. The pivot mount is configured to ensure that the optical aiming device returns to zero, within a ¼ milliradian in some implementations, after being pivoted between the use position and the storage position.