You know it is accurate when you trace your family back to the man to whom it was awarded, or who bought one from the national College of Heralds.
You have to go back to the middle ages to find your name's country of origin. In England, they started up about the time of the Doomsday Book. In Sweden, the late 1700's. Either way, you trace until you find "John the Baker, son of Paul" names his son "Michael Paulson" or "Michael Baker' instead of "Michael the Carpenter, son of John".
I'm not saying you can do that reliably, until they invent time machines, but that's what you'd have to do.
Coats of arms started so knights could tell each other apart when they were buttoned up in their suits of armor. They were given to individuals, not families. If, for instance, every knight named Smith used the same coat of arms, there would be a small army riding around with identical shields. It would be as confusing as a basketball game where both sides wore blue and every player was number 12.
The eldest legitimate son inherits his father's Coats of Arms. He passes it on to his eldest legitimate son, and so on; that's where the myth of a "Family" Coat of arms comes from. Only one person can PROPERLY (See below) have a given coat of arms at one time. People who sell T-shirts and coffee mugs, however encourage the gullible to believe Coats of Arms are for a surname. (The Irish and Scots have clans, which have badges, which are different.)
Below:
If your surname is Smith and you come from Shropshire, you may find that Sir Albert Smith, Sir Bruce Smith and Sir Charles Smith, all from Shropshire, all had C of A. If you do your research, you may find you descend from Sir Charles, but you are nowhere close to being the eldest son of the eldest son of the . . .. Now comes the question - Is using his coat of arms proper? Opinions differ.
Some say it is like demanding "your" room in the ancestral Smith estate in Shropshire, from the current owners - ridiculous and illegal.
Some say it is like wearing a Regimental tie if you didn't serve in that regiment. (Land's End sells those by the thousands to Americans. I would never buy one.)
Some say it is like wearing a Scotch Plaid shirt when you don't belong to that clan. (LL Bean sells tens of thousands of those; I have Lindsay myself.)
Some say it is as harmless as wearing a Detroit Tigers baseball cap when you didn't play for the team, or a UC Berkeley T-shrt when you didn't attend the University. (Or an Ohio State one, but as long as you're going to wear a University T-shirt, why not the finest?)
So, there's the facts and three opinions about using a "Family" coat of arms. You can make up your own mind, after you do your research.