My grandmother is 87. She was 50 when my grandfather died. She's still wearing her ring, and wears my grandfather's around her neck most of the time. She has never dated, nor did she want to.
Until recently, she lived in a very small town in So IL, before my mom moved her up north to be by all of us. A man asked her out about 10 years after my grandfather had died, and I asked why she didn't go. She said she didn't like him when she was younger, and nothing had changed now that she was older.
You'll know when the time is right to move/remove your rings.