I found an article in the Royal Society of Chemistry that described the processes they had been using to save the timbers, leather, iron cannonballs, and other artifacts recovered from the Mary Rose. Here's an excerpt as relates to the cannonballs:
"So, for example, preventing corrosion in artefacts made from metals such as iron, bronze and copper, including guns, powder scoops, nails and bolts, requires removing chloride salts. The most effective technique for doing this, especially for iron artefacts, is hydrogen reduction, which involves heating the metal artefacts to a temperature of 850°C in a hydrogen atmosphere. Although effective, this technique is highly controversial because it changes the metallurgical structure of the artefact, whereas ideally the artefact should be preserved in its original condition.
‘This is the only method that has successfully removed total chlorides from iron found in the marine environment, but we’ve stopped using it,’ says Jones. Instead, they’ve switched to other techniques, such as alkaline sulfide methods, although these tend to be much slower, especially for large objects."
