Does such a thing as a cat-proof stair gate exist?

[Borka]

I have a new rescue cat who keeps wanting to jump out of upstairs windows and although I can keep the doors or windows shut, the bedrooms are getting really stuffy, so I really want to be able to keep her downstairs some of the time.

The gates I've seen online don't look tall enough, does anyone have anything that works?

Not a gate, but you can get these screens for the windows. I use them upstairs, they've been cat-proof so far from my fairly hefty moggy and a 6 month old very lively Devon Rex.

What about those safety latch things that only allow windows to open a little and not far enough for a child/cat to fall out ?

Or keep the bedroom doors shut at all times, so if she goes upstairs she can't get to the open windows?

Those screens look good, Mantra, they might be the solution.

I've tried only having the windows open a bit (they have a sort of latch position) and having the windows open but doors shut, but it doesn't really get enough air flowing.

You can or at least could get a taller stair gate or I believe it's called a dog gate from Argos if you can put up with their ridiculous purchasing system. We had one once it's about a third higher than a normal stair gate. We have to put a normal height stair gate (to keep dogs downstairs) halfway up the stairs because we live in this ridiculous old house with a carved Newel post and can't attach the gate to it. Neither of our cats are able to jump it there, although both can jump fairly effortlessly another one, if there was food the other side, which is in a door way to keep the dogs out of the living room. Admittedly neither are very agile, but the super agile young cat we recently lost couldn't jump it either. I think they can't judge the landing side very well because it's half way up the stairs if that makes sense.
There is also a website of a company that make stair gates for odd shaped doors etc and a I think they made taller ones, and ones with cat flaps in, I think I found them by googling stair gates with cat flaps in! But I suspect they'll be more expensive that Argos.

I've got one of those flat cat screens and it seems to work well the couple of times I've had the window more than a cat width ajar - typically ordered it when we were in the midst of that heatwave this summer, and once it came it cooled down so haven't really needed it much since then! I've left it up so they get used to it being there and they haven't tried climbing the mesh (much).

Thanks happygardening, that's really interesting about the gate half way up the stairs. I've got a normal height one I can try it with, and if she can jump that I'll look at the Argos one.