Some clarification is probably called for here.
A deceased family member gifted some physical gold to us: bars, coins, etc.
A deceased person can't "gift" anything to anyone. There is a defined difference between a gift, and an inheritance, and that difference matters to the IRS for tax purposes.
If the items were left to you in a will, or if awarded to you in probate after their passing, then what you have is not a gift. It's an inheritance. It does not have to be reported on any tax return and you do not pay any federal taxes on it, if the value is less than $11.5M (I can't speak for state taxes, but for most states that tax personal income, the same holds true.)
The only value you need, is the fair market value of the item on the date the original owner passed. That will be your cost basis. You will need this cost basis only if you sell or otherwise dispose of the items in the future. The cost basis will never be taxed. But it will be used to determine if you have a taxable gain or loss in the future, in the tax year you sell or otherwise dispose of the items.
