Gods make miracles, mages cast spells. So the question can be turned upside-down like this :
What is the difference between a spell and a miracle?
A spell is an action on the world that follows a set of rules even though the source of the action is never truly explained (magicka and so). For instance, even if you don't understand how the energy comes out of your palm, and how the character feel when they draw magic to hold a fireball, you know that a water elementalist (kineticist in Pathfinder) will only be able to make water things, within their own limits.
A miracle is an action on the world that breaks any kind of rule and more importantly common sense. That is the main difference. In the real-world, splitting a river in half in a matter of seconds is considered as a miracle, as much as the act of multiplying bread is. Even though they vary in scale, they break our world known rules. And this makes them unexplainable, even by the biggest heads of the country, for centuries and millennias. Then your goal first and foremost is to make something that breaches into the thread of reality, making something truly impossible in regards to your world rules.
On top of that, miracles are often grouped into themes like gods in mythology are in charge of one topic (Poseidon : sea, Anubis : death...). It's simply because people put a face to things, and having one god doing everything makes them less clearly defined. If your artifact can make multiple things at once, it can be wise to group them in the same thematic to reinforce the creation of a myth.
Last but not least, miracles inspire most of the time pure awe. A strong effect makes this feeling sprout and reach the skies (as I bet your worries lies in), but! In reality, the roots of it come from the fact it's unexplainable, so you can create miracles even if people can reach a quite high level of power.
How can you make a miracle?
So the way to go is to breach a physical rule in a way which makes it totally unexplainable to the people of your world. You can add on top untangible and/or unescapable effects, as they're often related to mythology (like Fate or souls) and are things which are hardly interactible nor understandable.
To give two examples : In the quite-old-now game Planescape Torment, there is an enigmatic character who can basically kill whoever they want inside their territory, without constraint of time or effort (untangible and unescapable), and no-one could ever explain how they do this, even the wisest mage/priest (unexplainable). Without going to the extent of killing, you could calm one's deep soul (untangible) through a single gaze that can pacify even the most belligerent, angry warrior (unescapable), without any trace of magic (unexplainable).
That's a quick trick to make miracles, but you can use other extraordinary terms based on your context and world laws. The lower your overall fantasy and technology level is, the more possibilities you will be given.
Traps to watch out for
When looking for your miracle, don't look too much at the inherent mechanics of your world and forcefully try to break them, saying "this is like that mechanic but...". Doing so would make you risk facing people seeing it as a variant, and eventually find a plausible explanation to this or simply comparing to it. Stopping gravity in an area when a mage can lower it the same way is too close to an existing rule. Making as if raindrops of gravity make one's soul fly to the sky is far enough different from a simple gravity field, as much as in terms of strength as in the form it is delivered : You can have a grasp of what a no-gravity field would be like on the body, but can you explain what it would be like to have rain of anti-gravity droplets move out your inner-self?
Also, as is shown in the previous rain example, don't forget people's perception and feelings when faced to the miracle. This is a really big factor in order to fall in awe and gives lots of unexplainable things, yet it can easily be overlooked, especially if you inspire yourself from a pen-and-paper rulebook. If you think your magic as some kind of river, and magic is sent with a continuous stream of it, then a periodic, fluctuating wave coming from all around you would make anyone truly uncertain about the true nature of the action. Not because the effects are utterly different, but the way it is felt is.
Finally, to make a character look like a god, it should NOT be something your character don't have any control over. Miracles are actions, and if the entity behind that action is the item and not the person, then the godlikeness will be credited accordingly to the item, not the person. That's kinda silly, but it's one thing that makes heroes and gods different.