(no-one answered, so this is how I would do it if it were my problem...)
extract and analyze sufficient nectar samples until confident about the sugar concentration of the nectar ; quantitatively rinse out the nectary of the flower in question , quantitatively analyze for sugar(s) (concentrate by evaporation if necessary) ; calculate the nectar volume from the now known concentration and the now known quantity of sugar(s) .
I am unfamiliar with the morphology of the flowers in question, so I cannot judge how accessible the nectar is for extraction (or the precision you require); my suggested method seemed like reliable alternative involving a minimum of instrumentation, although it would require familiarity with analytical "wet" chemistry.