Must I pay self-employment tax for the Executor/Administrator Fee paid to a court-appointed Executor/Administrator for a deceased person’s estate?

No, you do not have to pay self-employment tax if you are not a professional Administrator. 

The IRS does not consider non-professional fees to be earned income.

Earned income is an IRS term for income that is obtained by participating in a business or trade.  Because you do not have a business or trade as a non-professional,  you do not have to pay self-employment taxes but it also means your income is not earned income.

"All personal representatives must include fees paid to them from an estate in their gross income. If you aren't in the trade or business of being an executor (for instance, you are the executor of a friend's or relative's estate), report these fees as other income.  

• You report it on Line 21 of Schedule 1 of the Form 1040.