Some Christian scholars say the new testament is the most well preserved document from the ancient world. Now, most of those scholars say it is one of the most, but in areas like this things tend to be vague as to what is the most of anything. Besides this, I was wondering what other documents are the most well preserved.
So, what other documents are the most well preserved and why?
Also, I'm interested in methodology for determining how well preserved a text is exactly.
When you say "scholars", I suspect you're overrating their expertise. Actual textual critics would be reluctant, at the very least, to make sweeping claims like that. Any text of any length, if it is transmitted by a manuscript tradition, will always have a non-zero rate of errors. The effectiveness of error-correction by modern editors is very hard to quantify except in general and fairly subjective terms.
Probably the simplest and naivest way of quantifying preservation would be to look at how many independent witnesses there are (i.e. branches of the manuscript tradition), and asserting that more independent witnesses means better textual criticism, and therefore better preservation. But that isn't the same as counting the number of actual manuscripts, which I suspect is what your "scholars" are doing. The textual tradition of the New Testament, say, has so many manuscripts and is so full of cross-fertilisation that there aren't really any truly independent witnesses. That makes very early witnesses (like papyri, the codex Sinaiticus, and the Vulgate translation) even more important than they would normally be for an ancient text. That doesn't mean the text is in bad condition -- it is indeed in very good condition, as these things go -- but a naive count of witnesses just isn't a good way of quantifying its quality.
But. Any original copy of a text has no transmission errors at all, by definition, since there is no transmission. So for example any inscription will qualify as 100% perfectly preserved, if it is (a) intact and (b) not a copy of another inscription. Intact inscriptions of any length are fairly rare, mind.
I don't know off-hand what would be a great example of an old, intact, long inscription -- the inscriptions I tend to work with are in verse, usually only a few lines long, and though they're old, they're not nearly as old as the oldest inscriptions in existence, which go back more than five thousand years.