AW hardshell case pictures:

Yamaha makes a special hard-shell case for the AW4416, which is available in the US now...  Riksmusic.com sells these for a reasonable price.

This case was custom made by TAJTI MONITOR of Hungary, price about $80 (USD).

Soft AW carry case: 

While I was in Japan, I decided to try and find the Yamaha soft case for the AW4416, (the one mentioned on the japanese section of aw4416.com)... Well, that proved to be pretty much impossible.  For one there aren't that many musical equipment stores in Japan, we're spoiled in the US by MARS, Guitar Center, etc.  I found a local Sumiya store that had musical instruments, and also carried the AW4416, but unfortunately they did not have cases in stock, and would have to special order one from Yamaha.  This would have been OK, except that the Yamaha factory was closed for New Year's and would not reopen until I had already returned to the US :(

So I had given up on finding a case.  On my way back to the US I stopped off in Shibuya (Tokyo) at Ishibashi music, where the usually have some good deals on used equipment.  Well it just so happened that they had a case for the AW in stock, although it was not a Yamaha made bag, it was specifically designed for the AW,  and it was only 6500 yen (about 65 US dollars) compared to 12000 yen for the Yamaha soft case.  They only had one in stock, so I bought it.  The quality of the bag seems to be very good with very durable straps that are stitched all the way up the side from the bottom of the bag, and double latches for the carrying strap in case one should fail.  The padding is about 1-inch thick on all sides.  The only thing I might have liked to see is some sort of rubber feet on the bottom.  There is no tag or indication of who the manufacturer is though, strange. Here are some pictures of it...