Methods and apparatus for machining substrates are disclosed, as are articles formed from the separated substrates. A method of machining a substrate having a first surface and a second surface opposite the first surface can include forming a first recess in the substrate extending from the first surface toward the second surface, forming a second recess in the substrate extending from the second surface toward the first surface, and removing a portion of the substrate extending from the first recess to the second recess to form an opening in the substrate.