There’s a scam out there that has been going on for a surprising number of years—probably around 30. The pitch comes from folks who claim to be following strict heraldic guidelines. For a nominal fee, they will provide detailed research and will mail out your family Coat of Arms or family crest, all with a speedy turn-around-time Yet another case of Caveat emptor (let the buyer beware).
Unless you have special circumstances, there is no Coat of Arms. In Scotland, if your last name is Bruce, Buchanan, McDonald, McMillan, Forbes, etc., you might have a clan crest on display, but that’s different. Coats of arms were never given to families, so there is no family coat of arms.
Coats of arms were given by a monarch to a person to identify him in batter at a time when suits of armor made them indistinguishable when the visor on the helmet was closed. The coat of arms was painted on the shield and embroidered on the loose short coat worn over the armor called a “surcoat” and enabled identification of friend or foe.
The ancient Romans used images like coats of arms on their shields, but these identified military units, not of individuals. The first sighting of medieval coats of arms is found in the Bayeux Tapestry from the 11th Century, where some of the combatants carry shields painted with crosses.
Coats of arms were generally used by feudal lords and knights in battle in the 12th Century. By the 13th Century, however, arms had spread beyond their initial battlefield use to become a kind of flag or logo for families belonging to the higher social classes of Europe and inherited from one generation to the next.
“In Scotland, the Lord Lyon King of Arms has criminal jurisdiction to enforce the laws of arms. In England, Northern Ireland and Wales the use of arms is a matter of civil law and regulated from the College of Arms and the Court of Chivalry.”
If, through genealogical research, you have found an ancestor who has a coat of arms, the genealogy has to be documented from original source materials and must be acceptable to the heraldic court.
If you’d like to read more on the subject, which includes, in addition to British heraldry, Irish heraldry, German and Scandinavian heraldry and other European countries plus the practice in Americas click on Wikipedia the free encyclopedia. From there you can further explore.