It looks like "Butterscotch" or "Buttercup"? I believe Vintage Roses carry this rose? Check out their website.

Royal Sunset, or maybe even Brandy, if this is an unusually dark shade of what it usually puts out.

I looked for it in my rose books, you have an "Amber Queen", a 1984 Floribunda from Harkness. I hope this posts, it keeps rejecting my follow-ups.

That's a climber, definitely, and it appears to be a Royal Sunset. One of Dennison Morey's great climbers from the years when he bred roses for J&P. Kim

Here is a link that might be useful: Royal Sunset

Thanks for the ideas. I could go crazy with orange roses apparently!

I think I'll have to rule out Amber Queen which does look right but I think this plant has been in the ground longer than the 80s. The previous owner thought it had been in since the greenhouse was installed in the late 50s or early 60s. The classy fence post is newer. :)

What makes a climber a climber instead of something that was pruned funny? Aside from the obvious trunks, this one doesn't put out any long branches. But it's had so much "shaping" I can't tell.

Not Butterscotch.
Butterscotch is more brown.

Amber Queen was my first thought, but as noted above, it's not a climber. I suspect Royal Sunset, which is a real beauty.

Jeri