Dunno if this is a balance, skill, speed or other thing..

[BleeckerSt_Girl]

Sometimes on a difficult uphill, my heart gets pounding too fast and I feel uncomfortable (mine is from exertion though, not panic). When this happens I do a little mental trick of pretending the top half of my body is in a yoga class and is meditating and relaxing, and I let my hips and legs take over the work.
This seems silly, and I don't even do yoga.... but it does work for me to some extent.
I also tell my but and hip muscles to take over from my quads for a minute- that helps too.
The third thing I do is to do with breathing...often when I'm exerting myself on the bike I notice that I've started breathing one breath for each leg stroke, both left and right. Not good. When I catch myself doing this I switch to one fuller more relaxed deep breath per side- like only with the right foot stroke.
I think concentrating on your breathing and thinking about a yoga-like state can help relax panic. Also be sure not to hunch over too much as you are contracting your diaphram that way and can't take in as much breath.

[Crankin]

With me, it's panic; not so much the actual climbing, but when I come to a stop light at the top of even a teeny tiny rise and there are cars around, I am petrified of hitting a car or not being able to get going because of the hill. It is actually hard for me to do this, even though I can climb up hills with 18% grades...
The way I solved one situation which was stopping me from commuting to work after we moved was to observe the road and traffic while driving. Knowing that I would be hitting this intersection earlier, with little traffic helped me calm down. I visualized what I would do over and over until I just got out there and I decided to commute one morning. I never had a problem.
However, I fully admit that I know lots of ways to avoid these kinds of streets locally. I've had a few moments of panic on group rides, where I thought, "I would never plan a route to go through this intersection, etc."
So visualizing helps and the breathing thing definitely will help with the climbing.

[OakLeaf]

yeah - there's a blind intersection on the tour my club puts on annually where you cross a busy road in the middle of a 14% grade. The first year I did that road on my old race bike, I was just lucky that there were some other riders ahead of me in the intersection who were able to tell me it was clear. (I know, I know, skip the lecture OK?) If I'd stopped at the stop sign, I'd have had to walk my bike the next quarter mile up the hill. I don't think that's an irrational fear!

y'know - steep intersections never get discussed in the endless threads about gearing and compact vs. triple. I know it doesn't really address CC's question and it doesn't help you once you're at the intersection on a particular bike - but making sure you're in your absolute bottom gear would help, and if there are intersections like that on one's regular route, that would definitely be a reason to opt for shorter gears.

[Crankin]

Yes, in the intersection I described above, I always had my bike in the granny, even though I didn't need to be for the climbing. It sort of gave me confidence that I could get started, make the turn, etc without killing myself. Even with just one foot clipped in...

[OakLeaf]

make the turn, etc

Oh, duh, of course that's the solution! Instead of trying to go straight up the hill through the intersection, turn right, and proceed on the intersecting road until it's safe to make a U-turn. Then you can get going before having to make another right back onto the original road.

Doesn't help if both the roads are steep, but normally only one of them is.

[beccaB]

CrazyCanuck-I panic if I have to stop and unclip going up a hill. I've taken a few falls, and I really hate that.