I found a ring. Is the appraisal fee deductible since it would be required to ascertain fair market value? If so, what forms are involved?

[Opus 17]

If you keep the ring, then your appraisal cost is not deductible.

If you sell it, you can use the appraisal cost as your "cost."  (Any time you sell property, you owe capital gains tax if you sell it for more than your cost.)

If you donate it to charity, you generally can't deduct anything for the value, because this is  something you found and did not buy, so you don't have any "Basis" in it.  And the appraisal won't be deductible.

The ring is deductible as a charity donation only if you donate it to an organization that will use it as it is -- a ring -- and not sell it for funds, AND only if you hold it more than a year.  That might be a museum if it is rare or unusual.  I can't think of any other kind of charity that would keep the ring as a ring but maybe my imagination is limited.  If the charity keeps the ring as a ring, then you can deduct the appraisal fee as a 2% miscellaneous itemized deduction.