Rosella, so glad your torment is over!
We went through a similar incident many years ago. A black short haired ex CPL cat we adopted ran up a very very tall tree in the school grounds adjacent to our house. She had the habit of following us on walks across the fields adjoining the school, and she ran up the tree for whatever reason, and stayed there all night!
If I remember correctly OH had to find some very long ladders, which to be honest were not all enough. Anyway it was a happy, but hairy ending. She didn't repeat it again!
These days my son who is trained to climb trees as a tree surgeon, (has a certificate to prove it), says the fire brigade don't normally get involved these days, a tree surgeon (presuming a tree is where the cat is) is often the cheapest option and quickest.
He spoke of a tree surgeon going up a tree which was close to another one, and when he eventually climbed up, he discovered the cat was in an adjacent tree! (He reads tree surgeon forums, like we read cat forums!)
I bet your OH will be wishing he had been there! (or not!)