I used to bury my goats on my land - but when the foot and mouth came, I understood that as an agricultural animal they had to be disposed of in a proper way (taken away and not buried on my land). Therefore thats what I have done, and assume sheep would be the same? I know horses are classed as pets and can be buried in their field.
I dread Bertie our pet Shetland boy going - he is such a character, and more like a dog than sheep. He must be 10 now, but in good health. Its when their teeth go, and they lose condition, thats the problem.
I usually have my goats shot here, before they are taken away. The last one was put to sleep by the vet, and it was, in my view, quick and no stress for the goat.
A neighbour had a ewe that lived until she was 16 - she was a pet, having being bottle reared. She lambed every year, having twins, and I remember her having twns even in her teens, which I thought was amazing. We were all worried when she was ill when she lambed the last time, but she rallied and recovered well.