Secretly put one ring in each hand and let the oldest daughter pick a hand.
Inheritance: two daughters/ two rings What is a fair way to decide who gets which ring?
There isn't a fair way, I don't think. Too many variables. This is what I'd do. I would do one of two things.
Have each ring remade for each girl. You pick the style and have the stones if there are any equally divided between both rings.
In your heart you probably know which ring you want to go to who. Just give them the rings as you see fit. They live with it and are grateful for such a lovely gift. Life is not always fair. If you really feel that one girl is being slighted then give that girl another family heirloom.
Sell the rings ... Spend the money on enjoying your retirement. Both girls get none of the money. Problem solved.