What to do with a Nun’s silver wedding band? I found the silver wedding band that belonged to a deceased nun. I do not know the family, but her name is engraved inside and dated 2-12-46. 

What does the Church teach about the sacramental status of these objects and how can I avoid blasphemy while possessing them?
From what I've read, I think that the wedding band given to a consecrated religious sister is given to her for the same reason it is given to a married laywoman.

Womanhood is fulfilled quite as perfectly in a life of virginal chastity as in human marriage. And that is why the Church's ancient and elaborate ceremonial for the consecration of virgins has for its climax the placing of a wedding ring on the finger of the newly professed nun. &quot;Receive this ring that marks you as a bride of God.&quot; She is wedded to Christ. And the union is fecund with souls.
The Cloistered Life of a Poor Clare

And, if so, I think it would have the same sacramental status as a wedding band.  Catholic radio host and author Lisa Duffy, writing for the The Catholic Match Institute, says:

Therefore, the Church does not mandate that wedding rings must be kept or cannot be sold. What  happens to a wedding ring is a very personal decision and is left up to the spouse who remains in possession of it

and with regards to selling it, she quotes the Catechism's part on the sin of simony saying that you can't sell it as a magic totem or that it's better because it was a nun's ring (historical reasons may increase the value, but not spiritual reasons).
My first instinct reading your question was that it should be melted down and disposed of on holy ground like you would with the ashes from old palms or busted blessed scapulars.  But maybe that isn't the case for wedding rings.

The Church provides us with sacramentals (primarily articles that have been blessed, such as rosaries, crucifixes, holy cards, etc. but can also be prayers), for the purposes of instilling piety in the one who possesses them.

So the blessing is on the person who holds the ring and the ring, it's not on the ring itself.