The title of this blog sounds a bit like an oxymoron. Stimulate and relax, how could that work?
It works because deep breathing stimulates the vagus nerve (one of the cranial nerves), which decreases your heart rate and blood pressure - increasing relaxation in your body.
To do this, inhale for a count of 4 and then exhale for a count of 8. Repeat for a minute of two. After that time, you should feel relaxed!
For Pilates instructors, you could incorporate this concept into your cueing of Footwork on the reformer. Inhale for 4 counts as the client presses the carriage out. As the client returns the carriage, exhale for 8 counts.
You could use light weight in the arms. Have your client inhale for 4 counts as they open their arms to the sides as they press the carriage out. Exhale for 8 counts as they return their arms and leg to the start position. The picture below demonstrates the inhale portion of this version of Footwork.
By the way, this might be better to be done at the end of the workout. Or to help a client find better focus with their workouts, perhaps do this sequence at the beginning of the workout. Let me know how it goes!