I had a unique experience a few weeks ago: two climbers in two oaks about forty feet from another, 60-70 feet up.
The areas we were working were leaning out over wraparound porch and house, so it was nothing beneath us the whole way down.
The other climber called, "man, it's getting to me today, a little nervous up here." and we were both able to have a moment of recognition of where we were, rigging big oak chunks way up.
As many said, it's not unreasonable to be aware of the risks that are at hand. This little acknowledgement we had that day, encouraged me through the rest of the climb. What I noticed is I kept checking the alignment of my carabiners, just making sure everything was sitting well and aligned before I made any major movements. Maybe a simple routine, like a program to kick in when anxiety comes: a small checklist to assess all the risk factors.
I climbed a snapped-top oak the other day, tied in to a compromised top with a split down it. I know oaks well, so felt confident. Up 60ft with no limbs 'til then. I took some time to re-set the whole system, and lanyard in before making the first big cut (25 foot limb section). I like to walk through exactly what I think will happen, then factor in what could happen, and have escape routes in mind, just like felling.
I agree with what many said, anxiety is not bad, it's a function of our awareness. My view is that it arises when the responsibility at hand begins to exceed the resource and security we have at hand. For us as climbers, it is our skills that provide that sense of security. Proper gear is required, yet ultimately it's an inner strength that conquers the anxiety. I follow a little prayer if I am really worried about something. Generally from there I can sense if it's a go, or I have more preparation to do.