I am no expert but I have come into contact with some very old pieces since I have been in the jewelry industry, and it is very hard to find someone who knows about very old pieces. Honestly I think your rings are much much older than 150-200 years old. On the side of one of your rings it looks almost like a mermaid is holding up the diamond in the middle. The Greeks were known for incorporating mythical creatures like this in their jewelry and art. Also some of your diamonds seem to be rose cut as far as I can tell. Rose cut diamonds hit the scene in the 1500’s I believe. Now if your cuts are older (which it is hard to tell) They could be older. I know you can contact museums and pay for an appraisal for very old items. My advise would be to search for museum that deal specifically with ancient jewelry. If your rings don’t turn out to be ancient they should be able to at least give you an idea of the time period so you can go from there.