Most SQL databases that support stored procedures have some kind of unit testing framework available these days, in fact have had for many years. Possibly as a third-party product or project, but the tools exist.

If you design your stored procedures right, they can be an abstraction over your data model. You then can change the data model without the stored procedure interface necessarily having to change (though in most cases, changes to the data model are usually done to support new requirements, which typically involve new or changing business logic as well).