So what if the other side makes its final offer before you're ready to make yours? If you're on the receiving end, you have to be careful. Understand the psychology of brinkmanship. A final offer is a bold move. If you test a "take it or leave it" ultimatum too aggressively, you may back a clumsy opponent into a corner. They won't know how to get out of it, and they'll dig in their heels just to save face.
A little deal-making diplomacy serves you better. For example, you can ignore the offer and continue to negotiate. Consider restating it as an aspiration: "I agree with you, and I'd also like to get this done quickly, but we still need to talk about..." If a deadline is involved, you may suddenly become "unavailable." Or you can try my favorite--a few open-ended questions. "What do you mean when you say `best' offer?" "Why did you decide to make your last offer just now?" "Under what circumstances would you make a better offer?" Listen carefully--the answers may give you just the opening you need.