I had a house fire, and my insurance coverage only covered about half of the cost to replace the items I had. Can the half that wasn't covered by insurance be claimed?

No. This would be considered a personal casualty expense.  Personal casualty losses are not deductible for tax years 2018-2025 on your federal return. 

 Depending on which state you live in, if they have itemized expenses with casualty losses as an itemized expense, you  may be able to deduct it on your state return.  

Which state do you live in?