...the very best modification you can make to this bike!
It always bugged me that Kawasaki saw fit to line the fairings and the fuel-tank's underside of it's quieter, smoother inline-four bikes (like my '02 ZX9R) with foam padding, but does ~not~ do this to our comparatively clankery 500 engine.
Inescapably, every machine makes mechanical noise. The more moving parts, generally the more noise you can expect. One advantage the shim-under-bucket designs have over us is fewer moving parts. (Though it's more a PITA to adjust the valves on this configuration, and that's not even taking into account that you'll have to do it to twice as many cylinders.)
I suspect this mechanical noise why Acrapovic, Muzzy and Vance&Hines are such successful companies: One popular way to mask that mechanical noise is with a louder exhaust note. But here is another way, one that will cost less and almost certainly save us money on tickets:

These are the Kawasaki OEM pads from an '02 ZX9R stuck on the inside of our beloved 500's fairing. They're invisible when the fairings are mounted on the bike and it sounds SO much smoother and quieter with these pads installed... like an electric engine, except now I can hear the stock exhaust note even better!
I just spent nearly $400 on a Works Performance shock, but this ~$80 gave me more bang for my buck.
Here are the part numbers, if you're interested:
39156-1603 PAD,SIDE COWLING,LH,UPP1
39156-1604 PAD,SIDE COWLING,LH,LWR1
39156-1605 PAD,SIDE COWLING,RH,UPP1
39156-1606 PAD,SIDE COWLING,RH,LWR1
39156-1607 PAD,LWR COWLING,LH1
39156-1608 PAD,LWR COWLING,RH
39156-1600 PAD,FUEL TANK,CNT1
39156-1601 PAD,FUEL TANK,LH1
39156-1602 PAD,FUEL TANK,RH1

And if you really don't care how noisy your engine is, here is a great video anyway: WHERE YA BEEN, JOHNNY?

 

Off topic just abit. What would you say was the total weight added with the foam inserts? Nice write up by the way.

 

They weigh almost nothing. Less than a pound for a complete set, including the shiny foil-lined fueltank pads.
I know that Kawasaki lines the fairings of other bikes, so your dealership probably has at least one sheet of the foam in their shop that you can see and hold.
They were made specifically for the ZX9R, so they look a little wonky and mismatched in our fairing, but they're invisible when the fairing's bolted on the bike. I did this to my previous 500R too, but several weeks had elapsed since I'd ridden the bike without the pads. This time I rode the bike to work this morning, then installed the pads after work and went for a ride tonight and got the full effect. Very smooth and quiet now!

 

That's a great write-up Chris. Maybe I should do that to the 250R.

 

So this stuff only goes to the plastics? Its pretty easy to put in? You have me seriously interested, does it cut out on some of the buzzing?

 

It's basically like large, poofy stickers. You just peel off the paper backing and stick it to the inside of your fairings and under your gas tank.
It makes the engine sound quieter and smoother, but buzzing is perhaps a symptom of something else?
Are you talking about tactile buzzing at the handlebars or auditory buzzing coming from down there? A common cause of buzzing noise with this bike is a loose exhaust header bolt. Just put some high-temp threadlock on those bolts.
There are possible sources for the buzz, a misrouted cable or hose rubbing on the fairing. But judging from the results of this foam damping, this plastic fairing is a very effective sonic conductor and reflector.
When I get my ear down next to the engine, I can still hear the clatter, but when seated on the bike... smoooth.