I use ground up orange peel scattered around the base. Also look for aphids, scale, or mealybugs, which the ants may be farming for their honeydew.

Or, you can buy 'Ant Stations' at a DIY or Garden Centre and put them near the plants. They do work!

Do the ants actually harm plants? I keep finding nests this year, a veritable plague.

They do in containers - the nests disrupt the roots of the plants, and they look VERY poorly! That's what happened to last summer's display in my large blue pot. I had to empty it out - nasty job!