A method and a machining kit for machining a bore hole into a shroud block are disclosed. The method includes designating a location of the bore hole on an exterior surface of the shroud block, positioning the shroud block in a machining device, securing the shroud block in the machining device, and machining the bore hole in the shroud block. The machining device includes a locating tool, a machining tool, a platform, a securing device, and a radial support. The radial support is configured to mate with a radial exterior surface of the shroud block such that a machining axis of the machining device may be aligned with a radial axis of the shroud block during positioning.