I define "the scientific method" as a process with four steps. 1: Systematic observation. 2: Looking for regularities in the observations. 3: Forming hypotheses to explain the regularities. 4: Experimentally testing the hypotheses.
(This isn't just me. Wikipedia describes the scientific method very similarly. This isn't me trying to cook the definition to make a point.)
Now assume, for purposes of argument, that God exists. And since lots of people use the word "God" to mean lots of different things, I'm going to define what I mean. By "God" I mean a being with personality - someone, not just something. Someone who existed before the physical universe, and exists independently of it - "outside" it in some sense, though I don't mean in a geometric way. Someone who created the physical universe, and who can, at his sole discretion, reach into the physical universe and change things. (You can think of this kind of like using a debugger - you can stop the program and change the value of a variable, with no antecedent in the flow of execution of the program.) And if and when he does, things actually change - it's not just a change in our perception; things actually physically change.
All this I ask you to assume for the sake of this argument. You don't have to believe it, but it's there for the argument to make sense.
And one more assumption: Assume that this God actually does change something, and that science observes it at step 1. The question is, what's science going to do with it?
They're going to throw it out at step 2, because there is no regularity. There's no pattern, unless God does this a lot.
But if they don't throw it out at step 2, the next problem comes at step 3 - forming a hypothesis. The way science currently is, "God" is very much out of favor as a hypothesis. But in our thought experiment, God actually is the explanation. Science is never going to propose the correct explanation for such an event.
But even if science proposes God as the hypothesis at step 3, the next problem comes at step 4: how are you going to test it? "Um, God, could you do that again? And, um, sign it this time?" You can't run the experiment. I don't see how you could run the experiment even in principle.
So in that sense, the supernatural exists outside of empiricism. This doesn't tell us anything about the supernatural; it only tells us that science is the wrong tool for investigating that.
But if God actually did reach in from outside and change things, even if we can't see it with science, we might see it with history. We might find historical record of God doing something. And when I mention that, one of the things that should come to mind is the resurrection of Jesus. It's like a giant flashing neon sign that says "Look over here. God did something."
You may say that the resurrection is impossible, and you'd be right. But therefore... what? What is your next statement? "Therefore it didn't happen"? I think that's the wrong position. It's impossible, but did it happen? Because the impossible happening is exactly the signature that we'd be looking for, if God actually did something.
And I think that, once you stop saying "impossible, therefore it didn't happen" and start actually, objectively looking at the data, the evidence is quite good. Not bulletproof, but quite good.
So in that sense, I think you can say that there is empirical evidence.