I have had a couple of castings where there has been a hollow void forming where a feed gate is adjacent to the end of an internal core (any thoughts?). I have repaired these successfully by casting in a very small quantity of bronze, using fire cement as a funnel and coffer around the defect. The bronze needs to be really hot. The surplus is cut off and ground down. The very small crucible was made from ceramic investment. Both repairs have been absolutely solid and undetectable.
This is probably re-inventing the wheel, but someone out there may be glad to know it.
I sometimes also get shrinkage defects, but welding is far easier than "burning in". In the industrial foundry ind. this is what it is called. It works like welding where the molten metal "burns" into the void and fusing to the casting. Large holes in casting used to be repaired in this manner in the past.
Post some photos of your casting please, I would love to see what you cast.
As far as repairing casting defects such as shrinkage etc. I use a carbon arc rod (Gouging Rod) with a standard arc welding machine for fixing shrink marks and crack that form in castings. (Although shrink marks point to other problems such as incorrect entry or metal that was to hot).
I cut off the runners and risers from the casting and use that as filler material for the hole – in that way you are certain that there will not be a colour difference between the weld and the original casting. The carbon arc process gives you plenty of high temperature localised heat and that helps the flow of the bronze into the defect. It also helps to put a few grains of borax on top of the weld AFTER you formed a button of metal in the casting defect. (If you put borax on the metal before you start you sometimes get small bubbles forming in the weld) Once you put the borax on you reheat the spot with the arc and the button will flow beautifully into the cavity to give you a clean and neat fill. Any excess material can be finished by normal fettling.
This process is quick and effective and generally gives excellent results.