I also wanted to add captions to picture frames and I 'knew' that it could be done because the Help article on Constraints talks about captions in picture frames, including a screen shot showing one, but I could not find an explanation of how to add them. Pasting the caption as content into the picture frame did not work properly. But with a bit of trial and error, I think I have worked out a way to do it:
Create a picture frame / Add a picture / Create a text frame for the caption / Go to the layers panel / Drag caption layer onto Picture frame layer / Select the caption and position it exactly where you want it within the picture frame / With caption still selected, open Constraints panel to control the behaviour of the caption text frame/ Click on the vertical double-ended arrow inside the small box—it will change to a dotted arrow—to prevent the caption from stretching or compressing vertically when the picture frame is resized. (It will continue to resize horizontally with the picture frame if the horizontal arrow is kept solid.) / Click on one of the dotted lines between the inner and outer box to lock the caption to an edge of the picture frame.
In the screen shot I have locked the caption to the bottom edge of the picture frame. With these settings, the caption always remains the same height but varies its width according to how I might resize the picture frame.
I hope this helps for anyone who hasn't already solved this little conundrum.