A Center Controller reported a small multiengine aircraft reported engine failure and landed at the nearest airport.

Narrative

I took the handoff from TRACON on Aircraft X with no indication of an issue. Aircraft X checked on my frequency asking for lower immediately and closest airport. I descended him to 13000 ft. then called [Sector] X requesting control. I also let them know he sounded in distress and they gave me control. ZZZ was the closest airport so I gave him a vector and descended him further to 11000 ft. On his descent I asked his nature of emergency and he said he lost an engine. Also sounded pretty stressed. ZZZ is tricky from that angle because to the SE of the field is an MIA of 13500 ft. The pilot told me he wanted to overfly the field at 11000 ft. but after concurring with my supervisor I only cleared him to 13500 ft. He reiterated to me he was an emergency to which I responded he can do whatever he needs to safely get the aircraft on the ground. I read the weather and NOTAMs and called the airport to him. He called it in sight and I cleared him for the visual. I had an overflying aircraft listen for any transmissions I could not hear. I tried to give him our phone number but he was not in a position to copy. In the moment I was afraid no one could reach him on the ground but I shouldn't have bothered him with that. The air carrier flight and another aircraft heard he landed but that he had popped a tire and was disabled on the runway. Five to ten minutes later flight service called to say he landed and I gave them a phone number to call in. No procedure changes I can think of. This was my first engine out emergency and I tried to provide all information I could. As stated above I think I did worry him with too much information. Next time I might let them focus on landing and worry about communications later.