It depends upon what is your puspose in knowing this data.
If for metering or cost, the morale of story is that the losses are so small that its within meter's error margin and it will not be worth measuring, as you could pay 1-2% more or less even if you have a 100% efficient xfmr and a less accurate meter.
If you need to know heat gain for sizing cooling or ventilation, the rules of thumb, 1.5 to 2% of the rating, is more than sufficient.
However in theory wattmeter measurement is only viable method, all you have to get is accurate meter/sensors.
The tranformer manufacrture can always provide with the no load losses and full load I2R losses, just ask them. (It is another matter they may also come with those data by typcial Watt measurement)
No load losses are constant and you can always intrapolate I2R losses at any load from 0 to full load as R remains relatively constant. (Purists: do not throw in change in R due to temp....not worth it).
In absence of data you go with rules of thumb, say for sizing cooling or ventilation...