It took almost 3 months to find out whether these were from a shipwreck or not. This weekend I found out that there is a better chance than not that these two rings came from one of the ships of the 1733 Fleet.
It is not officially certified. An expert on the fleet who has salvaged a lot of undeniable 1715 stuff said that he feels that they are from the fleet. That is good enough for me.
I cleaned both rings using methods explained by one of the legends of the Treasure Coast. Sadly, the smaller one came REALLY clean and has 925 inside. The large one is authentic. I am a little bummed.
I'm on the Treasure coast and we have a local pawn shop that has one of those X-ray guns that measure metal composition. I believe if there are certain percentages of zinc and manganese it may be modern. They can tell you, see if there is one in your area or perhaps a jewelry store.
Good luck!