Very surprised you haven't had any responses to this one yet. I'll give you what I know, and hopefully that will inspire someone who actually does it to add to or correct my post!
There are plenty of routes that go near to, if not directly over, the north pole. Many routes from Europe to western North America, for example. Take a look at a globe (not a map) and you'll see what I mean.
As for procedures, here's what I know from ATPL theory exams. Once you get close to the poles, you can't navigate with reference to "north" any more, because your desired heading will change very quickly. Instead, you use a "grid" system. You create a map of the polar area, and then draw a grid onto the map. The grid is usually oriented so that "grid north" is aligned with true north on the Grenwich meridian, but it doesn't have to be. Once you get close to the poles, you re-align your Direction Indicator so that it now points towards grid north instead of true north. You then navigate using this grid system until you're away from the polar region. At least, that's how it used to be done - I'm not sure how relevant this stuff is in these days of INS, IRS and GPS, but that's what we had to learn for the exams.
Now over to the professionals....
FFF
--------------