From the core rulebook's definition:
Minor artifacts are not necessarily unique items. Even so, they are magic items that no longer can be created, at least by common mortal means but still will likely have a great impact on the adventurers and societies through whose hands they pass. Minor artifacts are typically distinguished as artifact-level treasures of which multiple copies exist. This doesn’t mean minor artifacts actually prove significantly more common or less dangerous than major artifacts, though, or that GMs shouldn’t consider the same issues when choosing to add such potent magic items to their game.
From that we can say that Major Artifacts are items of legends, with tons of stories and mythologies around them, and are truly unique. While minor artifacts are simply magic items that cannot be duplicated anymore, you can't possibly come up with a formula to create them because the magic process was lost.
About balancing them, artifacts normally don't follow any balance rules, because they can be as weak as change your clothes at-will, to all powerful orbs of dragonkind, to devices capable of destroying realities.
Artifacts are truly unique items that can challenge the power of the gods, have godly powers, or simply have powers that even the gods can't duplicate.
When i create artifacts, i start from scracth, a simple +1 item, then i start adding properties. I pick a proprerty that i feel that makes sense, then i check it's value. And keep repeating that until i feel the item's level is appropriate to the level they will obtain it. The item doesn't have to be balanced, but it cant completely break the game either.
For example, last year we ran a ravenloft campaign from lv1 til 8, and as soon as 3rd level they found out they had to seek a certain sword forged in ice, with a silver blade capable of destroying undead and werewolves with a single strike.
At first, i thought this would be a +1 frost silver-coated longsword (+2 total enhancement, and a special material. I wrote that down and put it in my campaign notes.
But the campaign went on and on, and the sword was getting stronger in my notes just as the group kept leveling up, and the item's properties didn't feel epic enough in my eyes... I wanted something that once they identified all properties they would go "woah... look at this thing dude!".
And when they finally found it, they were lv9, and the sword had enough properties to be worth around 200 thousand gold pieces, with a bunch of unique mechanics, one of them being a pool of Ice Power, that could be used to fuel a couple of magic-related spell-like abilities the sword had, just like a staff, but that would replenish completely after 24 hours or one point after an hour immersed in ice. The effects went from simple things as a Orb of Frost and Hailstorm, to a 10 point (all charges) spell that was save or become a permanent block of ice.
The sword seemed overpowered, and that was the intent. The mechanics would balance themselves when they fought enemies that were resistant to ice (mostly undeads), and those abilities would need to be put to good use, the players would need to be clever on how to use them.
That Ice Power mechanic was more interesting to them, as it made it a sword that had staff-like powers, than the frost, keen or undead-bane abilities the sword also had at that level. They simply loved the idea of being able to summon blizzards at their enemies every day.
That's what you gotta have in mind when designing artifacts: What makes this artifact unique?
Paizo's Artifacts and Legends has a few guidelines on how to use and design artifacts to your campaign, i recommend it.
Earthdawn RPG will completely blow your mind when next you look at magic items, it is an old rpg (90's) that was made by the same creators of Shadowrun. On this setting, the more you know about certain magic item, the more powers you obtain from it.
If you know the magic sword's name, you now have a +1 sword, then later you find out that this sword was forged by elementals in the plane of fire, now you unlocked the Flaming property on yoursword. And later you learn from a book that this sword was used to slain the giant-king Aghmon of the Scarred Lands, now your sword is also a Giantsbane sword. And so on, it is a pretty cool setting by itself, but the read on how it handles magic items is truly Epic.
To define an artifact you have to ask yourself: What makes this item special?
If it has something that no other magic item has, you can call it a Minor Artifact.
Then ask yourself: What makes this item unique?
That uniqueness defines a Major Artifact