The Society for Creative Anachronism has a process for registering heraldry. If you complete it, nobody else can register the same arms, or the same badge, within the Society. Nor can they register arms that have less than two clear differences from registered armory.
This works poorly, and leads to bad results.
The chief problem is that they have accepted two late medieval innovations: the lamentable decision of Richard II in Scrope vs. Grosvenor in 1390 that a single clear difference between arms of unrelated families was insufficient, and the 1417 decision of Henry V that all arms in England most be granted by a competent authority. The Society goes even beyond this, idly supposing that arms registered in any kingdom must be free of conflict with arms in any other Society kingdom.
To understand the folly of this, it is important to understand the practice in England before 1390. The vast majority of arms were simply assumed by the bearer. They picked a design they liked and had it painted it on their shield. They didn't pick the same design of anyone they knew about, but in even a small country like England people from different regions could have the same design for generations before it posed a problem. And if they were somewhat similar, then only a fool would confuse azure a bend or with azure a bend or with a bordure argent. Even vision-challenged Sir Nigel Loring could tell the difference from long crossbow cast.
And of course, they didn't worry about conflicting with arms from different kingdoms. Not their problem.
So, if you look at the armory of England before 1400, most arms were pretty simple.Most of the time you had an ordinary, or a single charge, or three charges 2 & 1, or a field treatment. And almost all tinctures were argent, or, azure, gules or sable. Maybe you had a bordure in addition.
And this simple vocabulary was entirely sufficient, because you didn't require two by-Our-Lady clear differences, and a certain amount of duplication within a single kingdom was tolerated, because they often didn't meet.
Getting truly simple arms registered in the SCA is a real challenge. I've done it: azure, three sandglasses or. But even that is a bit of a cheat, since I chose an unusual but documented charge.
And that's my advice to you, if you want to beat the system. Pick a mundane, recognizable medieval object, put one or three on a field, and explore field and charge tinctures till you get one that isn't taken. Don't try a sexy mythological beast or a weapon. They've almost certainly all been grabbed. Pegasi and unicorns have been done to death, but you might try fishhooks.
But even if everyone follows my advice you still get armory that isn't very medieval. Because ordinaries, common charges and simple field treatments are still very difficult to register.
So don't. If you can't register a good, medieval design, all that SCA registration does is stop other people from registering a similar design. If you have a good medieval design you love, then display, and let those that dispute you take you to court of chivalry.
Interestingly, registered Society heraldry does show significant similarity with another system that followed similar constraints: Tudor heraldry. I don't much care for it, but I can see how it ended up where it did.