There are a number of techniques for measuring methane and there is not one that is farm superior to others unless you plan to use some sort of enclosed chamber. To me, it seems more reasonable to measure methane produced per unit of consumable product (milk or meat) rather that simply on the animal. Assume you have 10 cows, 5 of which are dry (not milking) and 5 of which are producing 10 liters per day. The cows producing 10 liters per day are apt to produce more methane, but not when expressed per kg of product. Low methane production is meaningless unless it is tied to some consumable product. If one looks carefully at the global data, one will see that countries with higher yield of milk per cow produce much less methane per kg of milk than countries that produce less milk. If we want to decrease methane output, we need to intensify yield so that amount of CH4 per kg of milk goes down!
Also, consider modeling the association between total methane production and population of bacterial subtypes. From this it could be possible to estimate methane production from stool analysis.
there is a way combined with milking and feeding , animals entering in the system of milking or feeding which measured concentrations of CH4 through the air that contineously pumped via the equipment to quantify flow CH4 and CO2 emitted during milking and feeding.
Kindly check the following RG link that includes a brief introduction to existing methods and model-based techniques for measuring and estimating methane emission:
Article Methods for Measuring and Estimating Methane Emission from Ruminants