The pictures they've shown of it, show sheep, with something like a 2 inch diameter plastic tube "molded" over the head/neck area and which sits just below the ears on either side, which monitors the air around the animal. [the tube is stuffed full of electronics and air sampling equipment].
Not sure about the rear end "monitoring equipment" - they tend not to show that too much when folks are watching the news - probably something similar.
As for cows - something similar is used.
The main interest of their research is that the methane tends to come from the animals guts, via belching, so for now I think they're more interested in the mouth/nose emissions,rather than the "farting" per-se.
So for now it should probably, technically be called a "belch tax". [ruminent animals emit far more methane via their front end than their back end - since the back end emissions have gone through a much longer process before being emitted].
Although each animal is a tiny emitter of methane, it all adds up when have 10 times the human population of them.
As for the worst natural emitters of methane around the world - thats been worked out to be termites, simply because there are so many of them and the way they build their hives.
However, Termites have been on this planet for far longer than just about any other methane emitter, so their "actual effect on/contribution to" global warming since the early 1800's has not changed much at all, - so no-ones got plans to tax them as far as I know - anyway, few people farm termites - they simply happen.