In my opinion, it is impossible to have a 100% sure Certificate of authenticity.
Except if:
-You bought the artwork directly from the artist.
-You have a COA made by him
-You have a bill of sale
-You have some document showing it is a gift from the artist.
If you buy an artwork with a certificate of authenticity ( COA):
1- have this certificate updated when you buy or re-sell the artwork.
a/ an expert may change his opinion about a painting. I saw a Parisian expert for Eugene Boudin changing his opinion about a painting he authenticated 30 years earlier and that he inventoried in his catalogue raisonne.
b/ Mr. X has made the certificate you have, but today Mr. X passed away and is replaced by Mr. Y. Mr. Y may or may not renew the certificate of authenticity.
c/ you need to be sure that the painting has the appropriate certificate: For example, for a painting by Amedeo Modigliani. You need to have a certificate of authenticity made by Ceroni; only 337 paintings have been admitted as authentic by Mr. Ceroni. The problem is our expert passed away .. You have other very important experts on Modigliani's work, Parisot, Restellini, etc. For example, suppose you have a painting with the COA from Christian Parisot, a very charming man and a great historian. In that case, you will have it very difficult to have it sold because he was accused of making fake Modigliani works (see links hereunder). Restellini (ex-secretary of Christian Parisot !) abandoned writing the catalogue raisonne he started since he received death threats. Yes, fine art has its" Dark side" very dark... http://www.independent.co.uk/arts-entertainment/art/news/modigliani-expert-accused-of-being-arts-biggest-fraud-8463883.html
2- Is the certificate of authenticity made by a gallery 100 % valid?
a/ if the certificate is made by a gallery of very high standing, they will have the certificate of authenticity made by the sole recognized painter. Often these galleries were exhibiting the artist in the past. Those galleries are of course, reliable, but I will always ask the original certificate since several scandals made surface recently and especially one of the oldest gallery in the USA, the Knoedler Gallery in NY: http://www.nytimes.com/2015/10/12/arts/design/lawsuits-in-knoedler-forgery-case-are-set-for-trial.html
b/ if the certificate is made by a gallery but is not considered as one of the top 25 galleries in the world, just consider that this certificate is completely useless.
You always should request the original updated certificate by the solely recognized authenticator and submit your buy to the contingency of providing this certificate if they don't want to have the sale canceled.