I have discovered what his new book is! It was completely by chance; I picked it up at Barnes and Noble just because it looked interesting, read it and loved it, then got suspicious when reading the author bio, then started seeing all kinds of connections, and finally had the brains to look on the copyright page, which confirmed it. (The full story of my detective quest can be found here.)
It's called The Magicians and Mrs. Quent, and it's by "Galen Beckett" (who shares a first initial and a last name with the heroine of The Last Rune, who was a physician like the classical natural philosopher Galen). It's the first in a fantasy trilogy, and it's inspired both in subject matter and in writing style by the novels of Jane Austen and Charlotte Bronte (though of course it also has a lot of Anthony's distinctive style and concerns, which is much of what made me suspicious). It's definitely worth picking up if you liked The Last Rune!