Our 2 cats have the run of our garden but can't get out of it. We cat-proofed it with a roll of chicken wire, some tie wraps and some plastic sheeting. One of them is very energetic and fearless but in 3 years has not managed to escape.
We used the chicken wire to create a ledge all around the fence and the plastic sheeting to put around a section of tree trunk (so they cannot climb past it).
It's great as they are confined to our garden but can go out and play without being ripped to shreds by the neighbour's dog (there are lots of big dogs in Aus and their teeth hurt - I speak from personal experience!).