I'm actually thinking of Inheritance as more like LOTR. I have a few theories of my own (only theories, and I doubt they'll be in the book):
Near the middle, Eragon and Saphira have a fight. Actually, it's more like Eragon shouting why Saphira chose him, because everything has been going wrong. It ends with him yelling that he never wants to see her again, and he storms off, leaving her in tears.
Saphira turns herself in to Galbatorix and Eragon finally realizes what he's done. He goes off to get her back, which is when he encounters Galbatorix. During that duel, Saphira enters, probably with Murtagh and Thorn, and, though she is bound to Galbatorix because of the ancient language, just before he kills Eragon she gets in the way of his sword, giving Eragon a chance to kill Galby. Eragon saves Saphira, of course.