I, personally, haven't had luck moving Salvias that large. I ended up taking cuttings from some and pulling-off side shoots from others, but the main plant didn't make it. Which doesn't mean yours won't... you just might want to back them up with cuttings, etc.

When taking the cuttings, do I cut from the oldest wood, or the newer branches? Should I use root hormone to help the transplant along, or other fertilizer?

Many of my salvias have been transplanted (some several times) with no problems. I always cut the top part back by at least 1/3.
Salvias are in the mint family, so they're pretty tenacious for the most part, although some are less hardy than others.

Rooting tip cuttings is easy. Just nip off a 6" piece of new growth (not woody), dip in hormone, and plant in potting soil. If there are large leaves on your cuttings, then I would cut them in 1/2 horizontally. Don't put the cuttings in full sun for at least a week, and keep them moist.

Thank you to all. I feel more confident now about the transplanting. Hope I can match your successes!!

I moved a 4' x 3' S. fulgens last spring without cutting any foliage back as sort of an experiment and out of pure laziness....;^)

I kept it well watered and it bounced back in a few weeks. I would not do it when it is really hot here, but during the cool months just about anything can be moved easily, without even cutting back.

The dryland salvia (e.g. CA natives) may be tricky to move and may resent transplanting, but I have never really tried.

Good Luck.