They wanted pictures of the dog at nose level, showing his head from the front and from the side.
Then they wanted a picture of a tape measure around the dog's snout, taken while the dog is panting, or while he's eating a treat. Here the tape measure is at 18 cm.
Finally, the length of the dog's snout, from just below his eyes to the tip of his nose. Cai is about 4 cm, so his muzzle length should be 5 cm (to add a little space in front).
They weren't sure about the measurements I had sent them for the circumference, and asked again for me to exercise Cai until he was panting, then place the measuring tape around his snout. However Cai does not pant a lot, and he closes his mouth any time he is uncomfortable or concentrating. Putting the tape measure around his snout both made him uncomfortable, and made him concentrate on holding still while I took a picture and then gave him a treat. So I took two pictures of the tape loop next to his face while he panted, and a few more of him wearing it, mouth closed.
The final measurements the BUMAS team suggested were 16.5 cm in circumference and 5 cm in length. I can't wait to get it!