The practice that grafters use is to hold the joint together with rubber grafting strip, tape, or grafting twine. Then they seal the entire graft area with warm grafting wax or grafting paint. Be sure to remove the rubber or twine shortly after the union has healed. Never allow the binding material to girdle the stem and seal it with wax to keep moisture and bugs out.

Here is a link that might be useful: Grafting

Thanks, rhodyman.

I've inspected the problem further and noted that the wound is not brand new and the wood a little weathered. Should I scrape or clean it in some way to make sure a union forms? If I remove any of the surface, I'm not sure the two parts will fit tightly together, but I might manage it. Or should I just rinse it off and join it?

What you will be doing.is grafting. Both sides must be alive. Look at any text or website on grafting,