Non-alcoholic substitute for madeira?

You can go with non-alcoholic red wine and sherry vinegar (or even better sweet sherry vinegar) if you have it handy, This is a very forgiving recipe, so you don't have to replicate flavors one on one and it will still work lovely. For example, you can use pomegranate juice instead of wine and it will yield a lovely sweet-tart flavor. Or you can use apple cider and a touch of red wine or malt vinegar. Feel free to experiment, as short ribs are a great canvas.

Or, a combination of white grape juice and beef broth.

Assuming that you want to eliminate alcohol completely, and not just the Madeira - they do make non-alcohol red wines, and that's what I'd opt to use. I'd also add in a touch of pomegranate molasses, or juice as well.