I would say put them in shade pretty quick and trim part of the leaves off to reduce transpiration. They may do better with inflated plastic bags round them. Shorter cuttings can do better.
Myles

Here is a link that might be useful: Passiflora cuttings

I've had good success rooting passifloras using florists' foam as my rooting medium. Take a two-node cutting, and cut about a quarter-inch below the bottom node. (Reduce the size of the leaf in larger-leafed varieties.)Dip in rooting hormone, and insert into a 1" cube of florists' foam (be certain you soak it thoroughly before you cut it into cubes!)until the bottom node is just barely below the surface. Place the cuttings in a shallow tray and add enough water to come half-way up the foam. Place tray on a solid surface in bright but indirect light, and cover with one of those translucent plastic storage boxes. This acts like a mini greenhouse, and keeps them from drying out. Check the water every few days, and NEVER allow them to dry out. Once you see roots growing out the sides of the cube, they're ready to pot up, but be careful to cover the foam completely---otherwise, it will wick moisture away from the roots. As the roots grow, they'll break down the foam.

I have NOT had good luck with P. vitafolia, however. ON the other hand, P. caerulea and 'Amethyst'will root in a glass of water!

Thanks for replying with such great information! Within a couple of hours of Myles' post, I moved them into a more shaded area and covered them with a plastic bag. I actually removed a few whole leaves from a couple of them (I learned later after reading the link provided by Myles that I probably should have just torn some of the leaf off). Anyway, the cuttings look about the same as in the picture. Some of the tenderer tip cuttings sagged a little as shown in the photo. msbatt, thank you for sharing your technique of using florist's foam cubes. I would love to try that when I am able to find another species of Passiflora that I can take cuttings of. I wonder why the vitafolia didn't work out well for you. I have heard of using bottom heat. Do you think that would be helpful for P. vitafolia?

I've had great results rooting vitifolia in plain water with some bottom heat. It also rooted well in the aeroponics chamber.

Here is an update on the P. vitifolia. I have four now alive and the other 3 died. In the picture I have an example of two - the other two look the same. They actually have rather tender stems leaves, although they are quite limp. It has been 16 days and they are not dried up, so they must be absorbing water somehow - hopefully that means I have the beginnings of roots. I am going to try bringing two inside to a bathroom with indirect light that gets good humidity from the shower, and leave the other two outside loosely wrapped in a plastic bag. The temperature outside is not a concern now in Central Florida. Is there anything I am doing wrong so far? Does anyone have a suggestion on what to do from this point to keep them alive?