TOO funny this came up! Not an hour ago I was outside covering my Walker's Low so the neighborhood cats couldn't roll on it any more! Last year the plant hardly bloomed at all because it was mashed so thoroughly by the cats.

What I did was take the liner out of a hanging basket and put that over the plant as a sort of cage. I secured it with some metal stakes. Lots of other things would work too, like chicken wire and those wire edging fences (only about a foot tall).
CMK

Plant some catnip (Nepeta cataria). Given the choice, cats will go straight to the catnip and leave the catmint alone.

My 3 cats have never bothered walker's low, and I have a lot of it. I do however, also have catnip. Perhaps torajima is correct in that if catnip is growing they will forsake all others. Worth a try - it works for me.

Yup! When I put in my first Nepeta "Blue Wonder" a few years back, the
neighborhood feral cat population soon reduced it to matted foliage and
balls of fur (they really DO roll in it! ). . . The solution, suggested by a farmer in Vermont: place several jagged rocks (size of your fist or larger) at the base of the plant - no more cats rolling around! A second solution I stumbled on accidentally: use Nepeta as an underplanting for roses, the sharper their thorns the better - those plants have never been touched. And so any feline fanciers out there won't think me a complete ogre: last year I planted a little division of one my nepetas out by the compost pile - they had found and flattened it within days! But it's not in the garden, so everyone's happy. . .

You don't need jagged rocks or sharp thorns. Plant catnip (Nepeta cataria).

I grow four different varieties of catmint, and the cats won't touch it... they always head for the patch of catnip instead.

Thanks everyone for the suggestions! I caught a cat in action today and one of my plants is almost completely gone! I hope it grows back. I think I'll do the wire cage/rock trick until I find some catnip to plant.

I have lots of Catnip I would be happy to trade. Take a look at my trade list if you're interested.

I grow catnip (Nepeta cataria) every year, and do exactly what christinmk said, put a circle of fence wire around it, about 1 foot diameter and 1 foot high. When the plant gets big enough, I remove the wire fencing. Although the cats (my one cat that goes outside and a neighbor's cat) still love to roll on it and mash it down. They never bother with the catmint.

I like to grow the catnip in an out of the way spot, it's very shade and drought tolerant, and it appears to grow like a biennial. It can reseed a lot, but usually I find it just pops up here and there, even the edge of the woods, so it's not too invasive.

I have lots of seeds if you're interested.

I have Nepeta Walker's Low in my front gar*den bed. I just moved it into more sun after having it in the back for 3 years. In the backyard, it was never bothered. So far, it has escaped in the front yard too. BUT, I had a Nepeta Kool Kat in the same bed, and that's toast. lol I haven't seen the culprit but something visited the gar*den and chose only that particular plant and mashed it to smitherines.