I have a couple of those, and I still shoot them now and then, especially when I get a chance to hunt cottontails behind my buddies beagles.
There are two things you need to do.
First, scrub the barrels out really well and then check for circular shaped pits inside the bores. Thats a pretty good indication that the lamination is about to give. The only thing to do there is sleeve it.
Second, ring the barrels. If they sound good, it should be safe. If they don't, hang it on the wall. That indicates that the soldering between the barrels is giving, usually the first sign of trouble in a damascus barreled gun. At that point, hang it up. The repair bill will be more than the cost of a new gun. Worthit, maybe if it's a Purdy or an H&H.
If you decide it's good to go, check your chambers.
I personally believe more of those old guns were destroyed by people putting shells that were too long in them than any other reason.
Modern 2 3/4 inch shells will chamber in both of my antique guns. But they have 2 5/8 chambers, and shooting the 2 3/4 shells will cause what amounts to a barrel obstruction along with all that it entails.
Restoring these old guns is never cost effective, but I'm working on a W. Richards right now. It'll be my third one, and I've not regretted any of them.