Methods of manufacturing or repairing a turbine blade or vane are described. The airfoil portions of these turbine components are typically manufactured by casting in a ceramic mold, and a surface made up of the cast airfoil and at the least the ceramic core serves as a build surface for a subsequent process of additively manufacturing the tip portions. The build surface is created by removing a top portion of the airfoil and the core, or by placing an ultra-thin shim on top of the airfoil and the core. The overhang projected by the shim is subsequently removed. These methods are not limited to turbine engine applications, but can be applied to any metallic object that can benefit from casting and additive manufacturing processes. The present disclosure also relates to finished and intermediate products prepared by these methods.