A manufacturing method includes forming one or more grooves in a component that comprises a substrate with an outer surface. The substrate has at least one interior space, and each groove extends at least partially along the substrate and has a base. The manufacturing method further includes forming one or more access holes through the base of a respective groove, to connect the groove in fluid communication with the respective hollow interior space. The manufacturing method further includes forming at least one connecting groove in the component, such that each connecting groove intersects at least a subset of the one or more grooves. The manufacturing method further includes disposing a coating over at least a portion of the outer surface of the substrate, such that the groove(s) and the coating together define one or more channels for cooling the component. The coating does not completely bridge the connecting groove, such that the connecting groove at least partially defines an exit region for the respective cooling channel(s).