An aft frame for a duct of a combustor includes a rail or radial projection that extends circumferentially around the aft frame and that defines an outer surface of the aft frame. A preformed cover plate having an inner surface is attached to the outer surface of the aft frame. A plurality of micro-cooling channels is formed within at least one of the inner surface of the preformed cover plate and the outer surface of the aft frame. The preformed cover plate extends across the plurality of micro-cooling channels.