1600's?

Hello I am unsure exactly how to describe this piece however I'm in desperate need of finding out where it may have come from my grandmother who is 83 years old and recently was diagnosed with lung cancer owns this piece she recently bestowed it to me. I am not necessarily looking to sell this piece I just would love to find out information for her prior to her passing. To her knowledge it was given to her by her father whom advised her that it had originally been brought over with one of our relatives on the Mayflower in the 16 hundreds I don't really know anymore about it I know that it was brought to an appraiser in our area and they were not able to tell us what the stone or and they were unsure of what the piece was altogether they wanted to send it out to have someone appraise it but my grandmother was afraid that something would happen to it and she declined and nothing has been investigated since. It would mean so much to me and especially her if we could at least find out where this piece may have come from and if it is in fact from the 16 hundreds. Thank you so much for your time.