There are many trade approved real certificate laboratories. GIA, the most known Diamond evaluator, does not appraise Diamonds for value, only certifies / does Diamond Grading, 4 C factors etc. If you receive GIA certificate and see value dollar amount in it, something is wrong.
There are many around the world. Below are the most commonly used in the trade. You can get referances from Jewelers Vigilance Committee, JA, JBT etc or simply from your local insurance company, who has list of regognized real trade approved evaluators at your local area.
GIA: The Gemological Institute of America
AGS: The American Gem Society
GCAL: Gem Certification & Assurance Lab
AGTA: American Gem Trade Association
IGI: International Gemological Institute
EGL: European Gemological Laboratory
HDR: Belgian Diamond High Council
Scan D.N: Scandinavian Diamond Nomenclature
CIGJO: International Confederation of Jewelry, Silverware, Diamonds, Pearls and Stones.
When ever you purchase a Diamond, receive any "certificate" with it, you have to see if certificate received is real or not. If not issued by trade approved real certification laboratory, it is often worthless and only one persons opinion...that does not mean your piece of paper is recognized by the Diamond trade as accurate. Since discussion is regarding safety of your money spend, there is nothing wrong simply in civil nice manner to ask prior purchase of any "Certified" stone: who certified this stone, is certificate trade approved certificate etc or just sellers own "certificate".
You have to also see this because your insurance. Some insurance companies are very quick to issue insurance if one has a "certificate" without backround check. Yet, if Diamond is lost or stolen, getting your money back might be hard. First thing insurance company will check if original value certification was real and from trade approved evaluator.