A method of manufacturing a component is provided. The method includes forming one or more grooves in an outer surface of a substrate. Each groove extends at least partially along the surface of the substrate and has a base, a top and at least one discharge point. The method further includes forming a run-out region adjacent to the discharge point for each groove and disposing a coating over at least a portion of the surface of the substrate. The groove(s) and the coating define one or more channels for cooling the component. Components with cooling channels are also provided.