Prune off the cold-damaged or dead plant tops in the later winter after they have helped insulate the catmint roots from frosts through the fall and early winter.
Shear off all of the dead or faded top growth down to the crown of the plant just above the soil line. Clear away all of the cuttings to prevent pathogens and to make way for new shoots to emerge in the spring.
Cut back the plant to half its size in the winter, when growing in mild climate that does not kill the plant tops. Reducing the height of the plant will create compact and dense growth form preventing an unattractive splayed out center. This pruning will also spur a flush of new green growth and early flowering in the spring.