faye,
This may not be the 'correct way' but it works every time.
I clean up the plant in spring. Take a big knive, cut a hunk off the mother plant, fill the hole with compost. Plant the 'hunk' where I want it.
That works fine for my Dropmore Blue and Walker's Low.
Basically, they're divide easily.

Libby

While you wait to divide, the AHS propagation book says you can take soft stem-tip cuttings in early summer.

My method for summer cuttings of any kind that tend to wilt is to take little cuttings,
put in a container, set the container in a plastic bag and put in the shade somewhere.

Nell

I usually do what Libby said. I divide it when it firsts starts up in the spring. I don't usually lift the entire plant, I just take the shovel and cut out a portion and refill the empty space with soil.

Cameron

Faye, I do root cuttings in potting soil. You can also use vermiculite or sand, or a mixture of any of those.
Don't obsess, just try some of whatever you have.

Usually I put about 3 cuttings or maybe 5 little ones in a gallon pot.
You don't have to fill the pot more than about 2/3 full of whatever you're using as planting medium,
as they're not going to stay in that pot much longer than it takes to root well.
You might want to put one cutting to a smaller pot.

I set the pot in usually a grocery bag and I loosely tie the top just to help hold in humidity.
I peek daily for the first few days to make sure the cuttings are not wilted
(in which case you can spray them with a little water in a spray bottle -- you did water them in well when you stuck them?)

Some sources say you can tug the cuttings gently to see if they rooted
-- I don't tug anybody, or I'll have a cutting in my hand, no root.
I take the pot out of the bag after a few days and just wait for new growth to indicate rooting.
Grow on for a 2-3 weeks after you notice new growth, gradually moving them to brighter light.

Maybe we'll hear from those who have more scientific methods, but this works for me.
Persian Shield rooted easily without wilting, bagged. Things like pentas and alternanthera that are not prone to be 'floppy' can be just kept in the shade
without bagging them up, just give 'em a spritz of water now and then.

The division method that Cameron and Libby use are for making two big plants of one for quick effect.
Cuttings are for making lots of little plants that will grow into big plants over a season.
I just like to see them grow, or I'd go buy the plants I need.

Nell

I have about a dozen 4" pots with cuttings of Walker's Low on my dryer. I find it's very easy to root. I take cuttings near the center of the plant, about 6-8 inches long, dip them in a bit of rooting hormone, poke a few holes with a pencil in the potting soil in the pots, place the cuttings in the holes, push the soil back around the cuttings so the rooting hormone makes contact with the soil and lightly water them. I continue to mist them for several weeks until the cuttings take hold. Don't be in a big hurry to tug at the cuttings to see if they've rooted - it takes a few weeks, trust me. :)

Oh, I mist them with a diluted mix of chamomile tea. Just put a tea bag in a pan of boiling water and let it steep for 5-10 minutes. When it cools fill a small spray bottle with the tea and mist your cuttings daily, sometimes more often depending on how warm your house is. You don't want the soil sopping wet, just damp. I don't use the plastic bag method - I haven't found it's necessary for catmint. You might want to experiment and try it both ways.

HTH!
Diana

It's a pretty hardy plant. At least it was for me. I hacked it in the spring AND fall and both worked well. Fall was better for my OCD side since I didn't have to look at floppy leaves for too long. But spring worked just fine. You can either dig it up, slice off a section or two, and replant; OR just take your shovel and hack off a section while it's still in the ground.

I've done both.

Tracy

Last yr. was the first time I tried to propagate via cuttings from roses. It was late in the season, so I was pretty much just experimenting. I took one cutting & put the pot on my patio step, right outside our sliding glass doors from the FR. Every day the same blessed squirrel came & dug it up!! The poor thing survived a couple of wks of this & then finally gave up the ghost! Anyone ever have this problem?

Carol