The Museum of the Frankincense Land had a shop on the premises that specialized in Omani crafts, the majority of which were incense burners like these. They were a bit more whimsical than what you find in Saudi Arabia, but basically the same thing and very popular, and not just with tourists, since everybody in this part of the world seems to burn incense. This shop also sold a lot of frankincense, and even myrrh. I asked the proprietor if I could take a picture of her with her wares, but she said her husband wouldn't approve, so I didn't.
I didn’t buy anything at this store since what I liked was far too bulky to carry for two weeks around the Gulf, but I ended up buying a sparkly incense burner in the souk the next evening anyway. That too was pretty hard to transport, but it got home to Riyadh with only a corner that broke off (cleanly, so we could glue it).