Tours are aboard small wooden boats which can easily maneuver in the tight spaces of the grottos. You do have to lay flat to get under some ledges but the grottos do not feel confining once inside. The grottos only extend inward enough to get the boat in. If you're daring enough then dive right into the sea. Your body will appear blue in the water and there are often smaller grottos that you can squeeze into for more speactular sights.
Many natural pools are near the grottos and are great for snorkeling.
Grotta della Pastizza has an easy clearance overhead. The crystal blue waters are unbelievable. Inside Grotta Azzurra. Now there's a low clearance. From a photo, it's hard to get a true appreciation of the intense blue water in this grotto.