A glassware-forming neck ring system includes a neck ring assembly and a carrier assembly carrying the neck ring assembly. The neck ring assembly includes a neck ring guide having a first forming aperture therethrough around a vertical axis, and a neck ring divided along a longitudinal axis into neck ring sections carried by the neck ring guide and movable toward and away from one another along the neck ring guide along a lateral axis. The carrier assembly includes a carrier having a body with a second forming aperture therethrough, longitudinally opposite ends, laterally opposite sides between the ends, and a channel extending between the sides, restricting movement of the neck ring assembly along the vertical and longitudinal axes, and permitting movement of the neck ring assembly along the lateral axis. A process of forming glassware includes carrying the glassware by a neck ring system through an entire glassware forming process from a blank molding station to a ware handler.