All of the vets that I have talked to send the animals to a crematorium. But then ultimately, who knows what they do with the ashes afterwards. Our local humane society has the animals cremated as well.
I would recommend a necropsy. That way you won't be guess and wondering what happend down the road.
I have burried several chins in flower pots before (mostly rescues), if you do it properly (enough dirst) they don't smell. 5 gallon planter works best for adults. I generally get a smaller bag of miracle gro (it's about $4-$5). Fill the planter up about 1/3 up. Place chinny inside, fill pot up the rest of the way. I traditionally plant a "Bleeding Heart" (Dicentra Spectabilis) plant with chins that have passed on.
Bleeding hearts are usually red, pink, and white, or a variation there of. Their bloomages (about 1" to 1 1/2") are shaped like a heart with a whitish "tear drop" coming out. They flower from May to August, require partial shade, and are perfect for flower pots because they like the water but for it to be well-drained.
If you want to cremate. you can have private cremation you can get your chins ashes back. Either put them in a flower pot, an urn, or they have stuffed Teddy Bear remembrance "urns" their is a vile that they put the ashes in and it goes inside the stuffed teddy bear. They also have cremation certificates.