Is it possible to restrict a singular Saved Search from being edited?

From non-Admins, yes. From other Admins, no. For non-admins, you should just be able to uncheck the "allow users to edit" box.

Hi thank you but this will technically still allow them to edit the search and just Save as. The goal is for select users/departments/Roles to be able to only view the results of one particular Search, but still maintain their ability to edit/create other searches.

I don't think that's possible without scripting