I have two approaches, both learned "the almost-hard way", i.e. by doing drills in grass and figuring out what worked and what didn't (and falling dozens of times while experimenting). I realized very quickly that the "bounce your tire off the other", a technique broadly recommended at the time in print and verbally, totally doesn't work for the hard tire-to-tire contact, and in fact I fell a lot of times trying to figure out if I was doing something wrong. I don't think I was, and I think the advice is for feathery light touches while in a pace line, not for the harder impacts that actually cause crashes.

If the rider in front is crossing my wheel I try to drive forward. The last time this happened it was in a crit, hard left turn, and the guy to my 1-2 o'clock decided he really wanted to tighten up his line and essentially swerve a lane or two to the left. My front tire hit his rear tire really hard as he crossed my bow. I was on the drops (naturally) and stood to reduce overlap and then powered forward with my bars (I didn't apply inordinate pedal pressure but I held my bars very firmly such that they wouldn't turn). His rear wheel slipped a bit, he recovered (because it's easy to recover from a rear wheel hit), and I didn't hit the deck. I found the bit on my helmet cam but you can't tell anything happened because, frankly, nothing happened. This is a situation that holding the hoods would be a poorer choice. When I say I held the bars firmly I mean I held them as hard as I could and really braced my arms hard. Maybe not a max bench press for me (180-200 lbs, depending) but a very hard effort (140-160 lbs bench? 140 lbs would definitely be on the low side). It's an extremely sharp effort meant to keep my line about the same.

In a hill situation you usually have a second or so to slow/coast/pause. This should buy you time to keep going on your normal line. On hills I'm typically on the hoods (yes I use the hoods) and when people in front of me stand I usually stand as well, especially if I'm close. If I'm already standing then I'll give some room.

(Of course this could be one reason I get shelled on climbs but I don't think so.)

The problem with trying to steer away from the offending tire is that if you're heading, say, 15 degrees left, and you try to keep the bike going straight ahead (0 degrees?) you'll quickly find yourself falling to the left. If you try to steer right, away from your original path, so say 15 degrees right for a total of 30 degrees off your original path, you'll fall even quicker.

So what I do is:
1. Goal is to stay on my original line. You want to keep control of your front wheel's direction etc so you can still keep control of your bike's steering. This in turn gives you the ability to balance on the bike.
2. If this means pushing the rear wheel in front of me out of the way then so be it. This requires adequate grip on the bars, which means a something akin to a death grip.
3. Rear wheel movement is recoverable so it's generally okay to hit the rear wheel if it means keeping your front wheel under you.
4. Yell at the rider for shooting his bike backward.
5. Direct him to the clinic page here.