PLEASE DON'T starve the owl! There is another way: metabolism rate is proportional to the number of O₂ + hydrocarbons → CO₂ + H₂O reactions in the body, which can be measured as the amount of CO₂ created during respiration. For humans, the CO₂ concentration in exhaled air is close to constant, so by inhaling through the nose and exhaling through the mouth into a bag (and not consciously hyper- or hypoventilating), one can get a very good measurement of one's metabolism rate in different scenarios (and the lag is seconds, not hours for nutrition!). This is obviously way more difficult to do with a flying owl (even in a wind tunnel) but perhaps a surgically inserted airflow meter could work, or a closed-loop wind tunnel with very precise measurement of O₂/CO₂ levels. Yes, a flying owl has CO₂ emissions, and so does a running human, but way less than a combustion engine.

Another idea is to measure the carbon and water emitted as weight loss (yes, you lose weight by breathing) but there are other factors that could skew the results such as sweat evaporation, skin shedding etc.

Just to add to your comment: calories in itself were a pretty good measurement for metabolic energy, because it is the energy needed to heat 1 gram of water by 1 °C, so something easily measurable to people at the time (roughly 100 years ago). The Joule was already proposed, but is less intuitive.

No one ever looks at the community before replying anymore, huh?