Hospedaje Mirella, located next to the church and part of the Agroturismo Network, makes it worth staying in Tenaún. The indomitable Mirella is an exceptional cook and is serious about making sure her guests enjoy the multicourse meals she prepares (CH$5000 to CH$12,000). She does curanto al hoyo, great seafood empanadas, cazuelas or whatever fresh catch the fisherman bring in that day.
On a clear day, you can see Volcán Corcovado across the Gulf of Ancud from the front porch. Mirella also runs a restaurant behind her home which is open for lunch and dinner from December to March, and can arrange boats to Isla Mechuque (CH$60,000 return, 45 minutes, minimum four people). Calling ahead is always a good idea.