The first thing I would recommend is reading my answer to What's the smallest change to physics required to allow magic?. Any question about fitting magic into our existing world benefits from being grounded in that sort of a mindset.
The second thing I would recommend is to invert the question. There are literally countless sources of magic you can pick from. Any one of them will meet your needs. The hard part is not picking a source of magic. The hard part is explaining why, for millions of years, we don't see magic playing a part in the world. Strange that it would be silent for so long, only to suddenly rear its head with goblins and fireballs (and all that jazz). You need a reason why magic is so muted in our world that we need answers like the one I linked above.
Even with that, there are myriad ideas you can pull from. So many, in fact, they bead like dewdrops in the morning:
I have no shortage of ideas. They are like dewdrops, distilling from the atmosphere onto my leafy green brain each morning. I'm fairly sure your brain is the same way. If you don't think you have any ideas, you probably just need to know how to look for the dewdrops. They're tiny, they're fleeting, but they glisten. (Howard Tayler)
Today, of all days, I happen to be exploring gongs. What is it that makes a gong sound like a gong? The particular curiosity I was looking at is why one "warms up" a gong before playing it. One lightly taps the gong several times to get vibrations going, at a very low volume, before a final strike which makes the wonderful splashing gong sound. If you warm the gong up before striking it, it sounds "brighter."
So why not pick this idea and run with it. Let's create the characteristics of a magic source that meets your needs with a gong like feel. Why choose a gong? Merely because that's the idea at the forefront of my mind today, so I feel like using it!
Gongs are nonlinear percussion instruments. This means they are instruments which depend on their nonlinear behaviors to create their sounds. Contrast this with a piano or a trumpet or a violin, whose sound is primarily grounded in its linear behavior, generating nice clean harmonics.
Fortunately for geeks like me, a great deal of the behavior of a gong has been worked out mathematically. We can even synthesize their sound with reasonable success. I like it when someone has worked out the math, because then I can steal the ideas they had, and apply them elsewhere.
One of the interesting behaviors of a gong is that its sound comes in three regions. At low amplitudes, the gong is mostly linear. It sounds like a bell if you play it quietly. This holds up until a particular amplitude where the vibration modes bifurcate, and we suddenly get a rich set of harmonics, creating a wonderful sound. If we raise the amplitude further, we enter a chaotic regime which is associated with the "splash" noise of the gong.
This is interesting to me for purposes of this magic system because there are clear phase transitions. There's a reason for there to be one behavior on one side of the fence, and a different behavior on the other. I also know, from experience, that one can make this transition by striking the gong. There's so many things which can be thought of as striking... a nuclear war comes to mind, but there's plenty of others. A powerful leader demonstrating his ego on a world stage could be sufficient to qualify as a "strike."
This analogy also has a convenient grounding in the opinion of many that the world wasn't this complicated in the past. If we've been ramping up the amplitude of our actions for a long time, it may have been that we were in the linear region for some time (where the world was simple and clear as a bell), and only recently entered the weakly non-linear region where all those complex pesky harmonics show up. This still leaves room for a truly chaotic sound that could be the foundation of magic.
So we've got a shape. Now all we need is a source of energy. I find magic systems which ignore energy to be pesky, because they don't play well with physics. Fortunately, we have a source of energy: the sun. I can guarantee you, without having ever met you, the wildest fanciest magic you have ever drempt of calls for energies that pale in comparason to the raw output of our Sun on any given day. Unless you are an astrophysicist, you have no concept of just how much energy that is. (For a glimpse: every second the sun releases more than 1000x times the sum total of all fossil fuel and nuclear energy reserves on the entire planet!)
So all we need to do is excite our gong with this energy. This is relatively easy to do with resonators. Helmholtz Resonators are a great source of prior art, which turn a stream of air into a resonator, but you can do anything you like with this.
So you have a system which was fed by resonators. For the most part, the system was forced below the weakly non-linear region, so it always responded simply. In the late 20th and early 21st century, we found a way to "warm" this gong up with the energy saved in fossil fuels. Finally, an event (such as a nuclear war), drove the gong into the chaotic regime, generating the "spashy" chaotic effects which quickly got named "magic" because they didn't fit with what we expected.
Well the system is slowly dying down now. Small transient pockets sometimes appear where the chaotic systems start to act merely weakly non-linear. Some of those whispers of the 21st century come through (at the same time, magic weakens).
From there, play with things. What if a group tried to make more resonators, keeping the gong chaotic, keeping magic alive. What if a group tried to silence resonators, driving it back to the 21st century? What if a group cut holes in the gong, creating regions of weakly non-linear behavior surrounded by substantially more chaotic magic? What if a group sought to make the gong larger and thicker (click the link for some samples of what that might sound like). Draw anything you like from the physics of a musical insturment, and see how it plays out in your world.
It's just an idea. But its an idea with an image. You can test if your magic system "sounds" right by seeing if it has the feel of a gong being struck. And yet, it can have the full backing of physics and mathematics needed to interweave it with 21st century physics.
So go use it... or other ideas. But the pattern I recommend is the same: come up with an idea for magic with an image, then explain why we didn't have it until after the event.
I picked a gong, because it happens to be fascinating to me today. Find something fascinating to you, figure out why it could have been around this whole time but not matter until after the Calamity, then just explore what it could become.