I searched for a bit and haven't came across any specific recommendations for a demagnetizer. I think I should get one at this point...
Never needed to do so. But the effect is big, I saw this at Omega Biel. You can easily stop the watch from moving with heavy magnetization. And it is really easy to demagnetize.
I automatically demag all purchased watches. I have found almost 70% move the compass needle at least 90deg. That enough to cause a problem. I've demagged a watch that just spun the compass needle around. It ran 7 minutes fast, then after, about 20secs. Further adj brought it right in. So here's my process. If a watch drives the compass needle less than 45deg but its keeping time(within 10secs), I leave it alone. More than 45 deg and I demag and readjust, even if keeping good time. Demag is easy, only takes about 30 seconds. Demagnetizer is under $10 on Amazon. These days even the little magnets that close your ipad case are strong enough to magnetize your watch if it comes in contact. BTW, I agree with the other post above that even a demagged watch moves the compass needle a little (up to 20deg or so)....the watches body of metal over the compass is interrupting the earths field.