You'll have to take it to a specialist engraver, who will use a laser to engrave on the glass. This'll doubtlessly be more expensive and, depending on the complexity of the mechanism, you might not even be able to see the inscription once it's been carved in.

They can best advise if the desired message will fit on the case back. Please note that returns/exchanges are not allowed after a watch has been engraved. If damage is caused during the engraving, it will invalidate the warranty period.

Some jewelers also offer engraving services for other materials like wood, leather, and glass. Make sure to check with the jeweler to see what materials they can engrave. Watch engraving is the process of carving or etching a design, message, or pattern onto the surface of a watch case or the back of a watch.