One of the most complex things to explain to newer autograph collectors is to explain what a certificate of authenticity (COA) is what what value it holds. The problem lies in explaining what a COA is and what it is not. At their best, for the most part, a COA is the hobby equivalent of the TSA in that is presents an illusion of security. The first thing that must be clarified is that a COA is not a legal document, regardless of its wording. Novice collectors tend to fall victim to the fallacy "Well, if it's in writing . . ." With very few exceptions, the best you can hope for if you get burned on a forged item if your money back. If you've given the item as a gift, resold it or had it framed, this isn't quite the great deal you'd initially think.
It's also important to understand that there really isn't a standard for these things. Seeing the 1990's problem with COAs from reputable sources being paired with bad items - or certificates themselves being outright counterfeited - many businesses switched to matching stickers/holograms and online databases. Good dealers sought increased structure and security. The worst dealers, scammers and forgers mimicked this.
Here's state first thing that new collectors and one-time autograph buyers need to realize: Absolutely anyone with a printer can create a "COA." Anyone can sign them. Frank the electrician can make one to accompany an autograph he knows nothing about. Forgers routinely print them off to accompany the autographs they just signed themselves. Businesses who don't specialize in autographs include them with items they sell in their misguided trust of shady dealers or collectors. These people might be incompetent. They might be thiefs. They could have good intentions and solid knowledge and simply get it wrong.
So, COAs are garbage. Sort of. The problem with this generalization is that it's not always true. The prime exceptions can be found in the modern sports autograph industry. Companies like Steiner, Tristar, Upper Death Authenticated (UDA) and many other companies, big and small, hold and participate in numerous large public and private signings. In addition to being the autograph authentication firm, they are the party obtaining the autographs, recording the information behind them. These are essentially assembly line autographs with the guarantee being an actual guarantee, because there is presumably no lingering doubt about it.
These certificates are worth something, because they dominate the sports collecting market. Take a $1000+ Michael Jordan autograph with UDA certification. Now take that exact remove the UDA hologram, certificate and database entry. Is the autograph still real? Yes. Is it still worth $1000+. Probably not. Even knowledgable Jordan collectors might back away entirely because of Jordan's long time relationship with the company and the widespread sentiment that you shouldn't touch any autographs from Jordan - possibly the most forged celebrity of the past quarter century - without the UDA authentication.
If I was to purchase a Tom Brady Super Bowl 51 autograph, I would not even look at anything that doesn't have Tristar certification. The second I was to exit Tristar territory in my quest for an authentic Brady, I'm immediately entering a field riddled with mines at every step. He's a forger's dream at the moment: A red hot athlete and a bonafide legend with a simplistic scribble of a signature that can be convincingly forged with minimal effort. Any authentic items will be buried under heaps and heaps of trash and then will only be conclusively identified (if it's even possible) by a very select few. That Tristar sticker and COA are absolutely valuable. The difference in value is hundred of dollars.
This contrast is what makes it so difficult to explain the value, or lack thereof, of COA to those who are new to the hobby. Good sellers and outright fraudsters alike issue them. What they represent requires hobby insight.