The accepted wisdom is that approaching to even within 100km of the city's outskirts (let alone the city proper) is akin to suicide. It's reasonably clear that there have been at least some efforts to probe the city's defences or Roland wouldn't be able to say, with confidence, that Neo is completely off his gourd.
Neo: I still have to go.
Roland: You'll never make it. In a hundred years no ship has been within a hundred kilometers of it. You'll never make it.
The Matrix Revolutions: Transcript
We can also note that the City itself has what could best be described as a robust (read massive overkill) defence system, albeit one that is relatively easy to defeat if one knows its secret, that it can be bypassed by traveling over it.
So what about them EMPs?
We see the EMPs being used a couple of times. Although they appear to be 100% effective against machines inside their range, their effective range seems to be only be about 2 miles, insufficient to reach the machine army waiting above Zion (which we know to be 2.5 miles under the surface). Once one is inside the Machine City, unless one had literally thousands of ships, and hence thousands of EMPs, the sheer size of the Machine City would defy almost any attack the Zionese could field at the present time.
Now, theoretically, if the Zionese were permitted to breed for another full generation and move up to full industrial-scale production of ships and materiel then Zion might actually prove a serious threat to the Machine City which is presumably why the Machines periodically kill all the free humans, forcing them to start over and over again.
Are the Zionese able to use other weapons?
Actually, yes. In the Animatrix short "Matriculated" we learn that a small group of humans is experimenting with trying to get machines (walkers and runners) to "convert". The end-goal appears to be to use these machines as shock-troops to attack other machines.