The LiCor 6400 CO2 gas exchange monitor not only measures photosynthesis, but will measure transpiration rates too. The only problem is that it is expensive and can be a bit tricky to use.
Just as A. G. Laney said. You can use portable gas exchange system, like Li-6400 (LiCor Inc., USA) or Ciras-II (PP Systems, USA). Ambient temperature, atmospheric vapour pressure deficit (VPD), assimilation rate (A), intercellular CO2 concentration (Ci), transpiration rate (E) and stomatal conductance (gs) can be measured simultaneously.
Although its precise and gives you a lot of information about the plant, as mentioned before a portable gas exchange system is an expensive investment.
A more simple (and also cheap) method can be found in Orsini et al. 2010 (doi:10.1093/jxb/erq188). Please refer to water relations section in this article.
In this method pots are sealed with plastic wrap after watering and pots are weight in an electronic balance. After a time period (which will be defined by you) pots are weighted again. Difference between two measurements gives you the water loss by the plant. You can use this data to calculate transpiration on a time basis (depending on temporal resolution of your data). Hope this helps.