Hiccups are caused by muscle spasms of the diaphragm. For humans, the way to get rid of them is to hold your breath and bear down (like a BM...) but that obviously won't work for the furbabies
I suppose the petting thing might work, but you'd have to push hard enough to calm the diaphragm. Drinking water, too, but I'm not sure how you could make him/her drink enough to get his/her mind off of it.