Most museums around the world are prohibited by regulations from authenticating paintings. In one very big European country the top museum was ordered by the government to stop authenticating because there was so much corruption going on.
If you paid a huge bribe your painting was authentic but if you refused to pay, it was rejected even if it was authentic.
In America the fear of legal liability runs so deep that museums don’t provide opinions anymore. You cannot take a painting to your museum and ask the highly educated curator what he thinks about it.
In the UK there is an important museum authenticating the works of the most famous of British painters. He was particularly prolific and therefore the odds of finding an authentic little drawing or watercolor are high. Yet, in the past 35 years the museum experts have rejected every one of the tens of thousands of drawings and watercolors they have been shown.
There are some competent private experts but they are often expensive and a majority of them act like a Prima Donna and are difficult to deal with. There is also a growing ear of legal liability on the part of these private experts and protecting themselves is more of a priority to them than determining if your painting is authentic.
There are Foundations and Committees and the majority of them are places of collusion where family members and the art galleries they partner with, get together for the purpose of trying to control, manipulate and influence the market for an artist.
Authenticating your painting is not high on their agenda and there could be reasons why it is not even in their interest to authenticate your painting.
The situation is worse in some European countries and worst of all in France; as usual; where any family member is considered by the law to be an expert and where he can destroy your painting at will, if he decides it is a forgery. It doesn’t matter if he is some nephew who never met the artist. One notorious widow of a famous Cuban artist resides in Paris and has had 120 paintings destroyed. Obviously it is difficult to show that your painting was really authentic after it has been reduced to ashes.
In Italy, it is usual for experts who have built a reputation to demand huge fees that are tantamount to blackmail, with a take-it-or-leave-it attitude. At the other end, rampant corruption makes it easy to obtain certificates from Italian art history professors with impressive titles such as a Ph.D. These worthless Italian certifications are so common that informed buyers simply refuse Italian authentications.
In Latin America, Eastern Europe and the Middle-east, certificates of authenticity are basically for sale.
In China, making fake things is an industry and making them well is a science. The only question with Chinese certificates of authenticity is did the forgery fool the expert or did the expert fool you?
Finally, there are a couple of commercial authentication businesses, like the Canadian restorer who keeps "finding" fingerprints in every painting he looks at. See the New Yorker Magazine article of July 2010 "The Mark of a Masterpiece" by David Grann.
There is the famous "Institut" in Paris run by the legendary family of art dealers that has also become legendary for unethical practices and all the dishonest things multiple scandals have revealed. A couple of shady outfits also prey on the unwary. One claims to use a special and secret (of course) computer method to determine if a painting is authentic.