My immediate thought was to put the plants in a chicken wire cage. But I don't suppose chicken wire fits into most people's interior decorating scheme. Shiny rabbit fencing?
Decorative iron scrollwork would be hugely expensive.
If you have window screens that you take out in the winter, maybe tape five together into an open-bottom cage that you could lift off for watering? Or check a Habitat for Humanity "Restore" to see if they have some window screens marked way down. I suppose that's still not a very classy "look". You could tell visitors that those plants had to be quarantined.
Cats could jump over or squeeze through a baby barrier or playpen.
Putting the plants on high shelves would probably be taken as a challenge - to knock the plants down and THEN eat the leaves.
