I'd give it back with a notarized receipt.
This way there's no foolishness later on with him 'claiming' that I still have his ring. When it's over, it's over; no remnants of a break up.
Give back the ring and get another one, that's real.
A real man that is.
For those keeping the ring, make sure to get a signed and notarized agreement so that he can't come back later and sue. It's not worth it. I've seen cases where the men sued even after they said she could keep it.
In some cases, when the woman moves on with her life, the man gets resentful / jealous and then files suit to get even.
It's not worth it, just to have a ring.
If he refuses to sign, get a witness and draft up a document stating that you gave back 'said' ring (and/or other items of his) and that he refused to sign an agreement of receipt of such. Have it notarized; list and/or take pictures of items returned to him. Protect yourselves from fools.