Ok random slightly relevant bit of info. If you're trying to melt amethyst, as you heat it it will turn into citrine. This happens long before it melts and if you stop the process partway through you get ametrine, which is a solid crystal that is part amethyst and part citrine. You could carve that into a ring and it would look cool but probably be incredibly brittle.

EDIT: I know they want sapphire but they can be yellow so it might have the look they want. And another hindrance to OPs idea is the fact that a gem quality sapphire large enough to be carved into a ring would be fairly expensive.