Thanks everyone. I appreciate the suggestions of online companies but I think the ones mentioned are in the US and I am in Europe.
However, inspired by some of the feedback, I searched a bit harder online and found a place (a local DIY chain) that will do a custom-cut acrylic mount (front, back and clips) for about 40 percent of the cost of the other place.
I had several oversized posters to frame and the custom cost was more than I wanted to invest. I opted to do it myself by mounting the posters to hardboard with spray adhesive. I then made my own frames with 2-1/2 x 3/4 strips of wood screwed together at the corners and spray painted black. I then tacked the hardboard to the frame from the back. I think I spent less than $50 for supplies.
At the time of the 1994 Northridge earthquake I had an apartment filled with gorgeous framed vintage travel posters, a collection that took years to put together one very expensive (glassed) frame at a time, as I could afford them. All but one smashed to bits, and the one that survived, I broke while trying to move it out. I never had the heart (or the funds) to replace them.
Another idea for the OP: lamination. I have a very large (48"x60") map on my wall, from a custom map shop whose name I’d be happy to share, which they printed and laminated in a low-gloss finish. The lamination is heavy enough that the map hangs perfectly flat on the wall, just tacked on the top edge. I’m very happy with it. This job was just $150 or so, and I’d expect they’d be happy to laminate anything you sent them rolled up in a tube, and send it back to you for cheaper than that.