There is no shortage of heraldic bucket shops selling random coat of arms to any fool who happens upon their cart at the local mall. Not so in England, where the College of Arms properly governs all coat of arms. Founded through royal charter by King Richard III, the College of Arms has been determining what is and what is not "done" in heraldry since 1484.
The legalization of same-sex marriage in the United Kingdom earlier this year has proven to be one of the thornier problems facing the College of Arms. There's a 500-year precedent for how men and women's coat of arms should merge when they marry, but what do you do when two men or two women marry?
The College of Arms did not last half a millennium by shying away from changing times. And so, for the most part, they are treating same sex unions as they do traditional marriages, albeit, with a few design tweaks.
According to the standard rules of English heraldry, when a man and woman get married, their arms become "impaled," or joined together, on a shield or banner, splitting it right down the middle with the husband's arms on the left (dexter) side, and the wife's arms on the right (or sinister) side. If a woman is marrying into a family with a crest on top of their coat of arms, they wouldn't use the crest. The logic here is that women don't go to war--even today, women are prevented from joining the British Armed forces in roles where their "primary duty is to close with and kill the enemy"--so women would not have a helm that they could top with a crest.
To accommodate same sex marriages, the College of Arms has had to make a few tweaks to these rules. When two men are "impaling" each other (their words, not ours), the College has dictated that each husband must have his own arms on the dexter side of the banner, and his husband's on the sinister. Both men must wear, on top of his arms, his own family's crest--and not that of his husband's. This will allow two husbands in a same sex marriage to distinguish their own combined coat of arms from one another's.
As for two women marrying each other, it's basically the same thing, with one exception. In British heraldry, it's possible for a woman to be what is called a heraldic heiress--a woman with no surviving brothers or male relatives. If a heraldic heiress marries another woman, the other woman's arms will be placed "in pretence" in a smaller shield over the heiress's arms.
Even if the College of Arms' mission sounds like it belongs more in Game of Thrones' Westeros than in the modern world, it's compelling to watch an organization so firmly rooted in the conventions of the late medieval period adjust to radical shifts in matrimonial law. If only all medieval institutions--ahem, Catholicism--were so nimble.