Wow...I was in Carmona a scant month ago. Yes, there is a Carmona in Cantabria. viamichelin.com brings it up, if you want to see a map.
Here's a photo from "El Diario Montañes:"
photo It is a beautiful Cantabrian village, very small, with traditional stone houses and architecture. the setting is magnificent. the drive there, form Cabezon de la Sal, was beautiful. Great hiking around there as well.
I do not think there is a parador there, rather there is a
posada (an inn) where we stopped for a cup of coffee.