At the moment there is not one single international body to certify diamonds.

However the largest and most internationally recognised is the GIA (Gemological Institute of America) although there is the European CIBJO who have affiliated national bodies such as the London Gem Lab, these are as stringent and just as good as the GIA, however their certificates are not as internationally recognised.

There is a chance that in the near future agreement will be reached on an international certification.