[Legate of Amon Lanc]

With what has been already said, I would consider the last remark Inziladun made for Sauron's fate as significant, however it's likely "metaphorical" here, Sauron would not have, I think, gone into the Void immediately after his final demise. I believe he remained around, but in such a poor state that it was even weaker than before when he lost his body after the Last Alliance, and now he definitely lost any chance of ever regaining his power, with the Ring being lost.

As for Saruman though, this always made me wonder too. In some ways, I like Findegil's interpretation. However, it still remains a question. The only thing we know for certain is that Saruman was rejected by the Valar - for either good or bad, that is, he would not return there among the Maiar in Valinor, but not even would he face a judgement from the Valar there (like Morgoth did). "In good and bad he belonged to Middle-Earth" now? Being rejected from the West, even from being judged in front of the Valar, is of course a judgement itself - and a pretty considerate one. The wind which dissolved his spirit made it clear. "Silence means judgement," as one Rabbinic saying goes, and I believe this would be exactly the case.

What exactly I have in mind: I think the Valar just decided not to do anything when Saruman's physical body was destroyed. What does it mean? Let us imagine the process of sending the Istari as some kind of a "contract". Basically, it was a job, so we can imagine it like a job contract. The Valar say: "You are going to Middle-Earth, for that, you will have physical bodies which can be harmed etc., and once you are done with your tasks, you can return here and you'll be again transformed into your immortal existence." That's all right, but of course accidents could happen, in such a case, I believe - and as we saw with Gandalf, in a way - the spirits of dead Istari would return to Valinor and would be given back their previous form of existence - only they would not be able to accomplish their task anymore. With Gandalf, he gained a special permission, when such a thing happened, the Valar's superior himself allowed him to go back with a new body. With Saruman, I believe the case was just different, where Valar actually denied to dead Saruman even to return back to Valinor - they cancelled their part of the contract. Even though the "contract" would have originally made it possible for the Istari to die during their stay in M-E, but they would be then still received back, in Saruman's case, not even this was made possible.

What lead me to think like this is the fact that Saruman's spirit was at first looking expectantly to the West - I don't know how it seems to you, but to me this looks like a kind of turn of events, because this would be probably for the first time in many years when Saruman had ever looked into the West (with the intention to expect some help from there). But: "We cancel our contract, we don't know you anymore", that was basically the meaning of the wind from the West, if it were set into words (and one could well imagine that Valar could support this decision by saying also "...because you obviously canceled the contract from your part already some time ago.")

And so, Saruman basically died like any other creature bound to Middle-Earth, with the single difference that now his spirit did not have a home to go to. Elves go to Mandos, Men go beyond the circles of the world, but Saruman - like Sauron - was rejected his home, the place where his spirit should belong to after his death, and now he was, indeed, I believe doomed to remain in Middle-Earth as a formless and powerless spirit. And in fact, to react to first post of Inziladun's, I believe his case actually was the same as Sauron's, only for different reasons. One was bound to M-E because of the Ring, and it was destroyed; the other was bound to M-E by physical body of a man-wizard, as a part of a contract, but he was rejected the possibility to return to his spiritual existence in Valinor, and so again, when the body was destroyed, nothing remained except for a formless and totally powerless spirit.

So they both were sentenced to roam the Middle-Earth in the long ages... and perhaps still wait for their final judgement. I think this could have given them both a long time to think, and it would be interesting to speculate if their ways would differ in any way here - for I believe it was said that Sauron would join Morgoth in Dagor Dagorath, whereas we probably don't know anything about Saruman, unless I am mistaken? - Anyway, they would probably both expect the final judgement yet to come, though I wonder if in the end this bodiless stay in Middle-Earth wouldn't be considered as a sufficient "purgatory" - and probably only after that, we shall see (cf. the Dagor Dagorath question above).