Largest caliber I currently have is 338/06 so I'd load that up with Nosler Partitions and feel well equipped. Backup would be my old trusty 4 5/8" Super Bhawk 44 mag.
Polar Bears are going to kill and eat you if they get the chance ,bigger is better with them IMHO. I a'm a great shot with my CZ 550 American 458 Lott and open iron sights. I'm a'm confident a 500 grain 458 will give me a good chance of stopping a Polar Bear . I a'm not recoil shy . Chances are your only going to get 1 shot any way B 4 you become a lite snack for the Polar Bear .
Up close and personal which means in camp and out doing whatever it is I am doing then not a rifle but a shotgun, either this semi-auto or one of my pump actions. Slugs all the way.
If I was deliberately hunting them than any rifle from my 300 WBY on up. 180 gr Core-Lokt SP have been working for me since the 70's, see no reason to change now.
I'm thinking a 450 Beowolf or the 50 Bushmaster and the 50 caliber 1911. Also 2 good dog to give you a heads up just a tad sooner than later. The biggest thing I would pray for is not to have the zipper on my sleeping bag freeze shut you may laugh but I had this happen once when I was delivering a load of Christmas trees in Canada one year. Had a good bag ****ty heater in my truck. LOL
30-06 200gr. SBT 2700fps/3200ftlbs should be enough to take a polar bear down. If not, thats all I got that would kill one so maybe I will just shoot whitetail.
At 2,740 ft. lbs. for the .308 180 gr., or 16% more power than the regular .308, let's call the .30-06 AI the .308 MAGNUM. It'll get'r done and without disconnecting a retina or dislocating a shoulder...