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If I have a tree on a lawn, for example, and I add a cast shadow on the grass, how can I accurately depict the shadow if it hits a vertical wall and climbs upward?

Make a new layer with a picture from tree, scale it, convert it to BW (Colours / Desaturate) and set the the layer mode Opacity to 60%. If needed, use the 'Perspective Tool' to adjust. 

[attachment=9364]

I would not worry too much about the shadow, there are lots of variables involved, the position of the light source, distances and angles.

For a made-up situation it might go like this: https://youtu.be/rb_8VJrsb84  duration 1' 40"

I was thinking of something a bit more realistic like this from Photoshop, but then somehow bending the shadow to climb up the wall.

https://www.youtube.com/watch?v=q_GOfAc3...nYadlovski

Also, see this starting at 18:49--this is what I want to do---

https://www.youtube.com/watch?v=HyAqx6VG...chUpSchool

If you look at the geometry of things the shadow (from the sun) of an object on a vertical wall is just the shape of the object, where verticals remain vertical. If the wall isn't perpendicular to the light rays, you get a deformation which is what you would get with the perspective tool. The ground shadow is also a perspective transform. In the following example:

• The shadow on the wall is just the shape of the object, shifted down and with a perspective to match the wall. The bottom is cut where the wall touches the ground  (at half the trunk height)
  
• The shadow on the ground is another perspective transform where: 1) the base of the tree is kept, and 2) it intersects the base of the wall where the wall shadow is cut, and in a place which is roughly at half the trunk height. As you can see from the branches in the top right, this is a very elongated perspective (in a real image you would cut these off of course.
  
• You can probably do the two perspectives in the other order, for instance if you have strong constraints on the ground shadow.