I have a nice Savage 99 in 250-3000, but the rotary magazine seems to have weakened from age/use (all the rounds in the magazine won't chamber). I heard there is an adjustment (screw?) that does not require removal of the magazine, which is risky. Does anyone know that procedure?

I had an old 99 G Model that han't been fired in a very long time. I noticed that the magazine rotated slowly. I Made up some dummy rounds for the rifle, and after a little while running the dummy shells though the magazine, and chambering the gun functioned properly. Hopefully this will be of some help to you.

It is nutso tricky thing to do. I removed the rotary magazine and retightend the spring by rotating it and inserting it back in while having a wood dowel rod keep it from unwinding stuck into the chamber.

I have a 1941 vintage 99. I don't have a clue how to do anything inside that internal rotary magazine, but I bet it's tough.
If mine were to exhibit the symptoms of a "weak" rotary spring..the first thing I'd do is open the action, hold the rifle upside down and hose out the internals with a can of hi-pressure degreaser. Flood it out good. Part of the issue..(maybe the whole issue) could be an accumulation of DECADES of oil, grease,and contaminants. For a long time...people who didn't know better thought it a good idea to hose the inside of firearms with WD40. That's just one example of a product that can lead to this kind of problem. I've seen revolvers for example that appeared to have weak hammer springs...but just needed to have gummy built- up residue removed.

Depending on the model: If you have a window counter the take off the forend, take out the window counter screw..Using a pair of needle nose pliars insert the points into the notches in the action that face the forend that you got to by taking off the forend..twist the pliars i until the number 0 comes up in the window, that would be 1.5 or 2 turns and in your case maybe 2.5 turns just have to keep trying until it works, holding the pliars at the chosen station reinsert the screw pin, try the gun. some 99s don't have a window counter so just use the 2.5 turns and reinsert the threaded pin, its a half threaded pin and the rest is just a pin without threads...add a half turn at a time until it works. Some models have a silver 3/4 moon like spring, that you must squeeze close and remove to do the job..

Usually this comes about because someone took it all apart and didn't put it back under the correct tension so it won't turn properly.

Its pretty hard to explain on paper, easy to show someone how, so the best bet is too take it to a gunsmith, I would not think he would charge you very much if at all...its a very simple procedure..