My current cat enclosure is no thing of beauty. It's a large chain fence link dog enclosure, with many widths of 1/2" harware cloth wired together over the top, and also wired to the top of the chain link. I have brick all around the bottom - it wouldn't stop a persistent digging predator, but the cats would have more than enough time to escape indoors. Their access is by means of a cat door set into a window, which leads to a boxed in ramp, reinforced with 1/2" hardware cloth.
When we move back to St. Louis, their enclosure will be like a large screened in porch, but with 1/2" hardware cloth instead of screen, and railings on the outside of the hardware cloth, to stop any really large predator from potentially throwing himself hard enough against the hardware cloth to loosen it from its framing.