So my Bianchi has a newer stem than anything else, and I have a feeling the clamp size is too big for the bars.

The stem is a Cinelli that does not have a slit anywhere where it grabs around the bars. It is solid, and I'm not exactly sure how it operates.

Here's the history:
It's creaked ever since I got it, but didn't slip. I torqued down the clamp bolt pretty good to no avail so I took the stem out and cleaned/lubed the part that goes in the steerer tube, and loosened the clamp bolt and cleaned and lubed the bars.

There were some aluminum shavings on the bar before I cleaned it.

Now the bars won't stop rotating on me, even though the bolt is on very tight. It must be the wrong size clamp.

Now my question: what diameter are Mod Fiamme bars from the early 80s? Could I shim this with a soda can or an off the shelf shim somewhere?

Sounds like you may have a Cinelli 1R stem. It is most likely 26.4. The bars you are using are 26.0. I would not recommend shimming. You may have cracked the wedge that acts as the clamping mechanism on the 1R, as well.

Is this the stem?
https://www.classicrendezvous.com/Ita...Cinelli_1R.htm

You didn't post a photo, but I suspect the stem to which you are referring is like this one.

It uses a bolt to press a ridged wedge against the stem. This stem is designed for bars with a 26.4mm diameter at the sleeve. If you're getting that much slippage your bars are probably 25.4mm instead of 26.0mm or 26.4mm.

I would think a shim of something .5mm thick would work, but I don't think an aluminum can is that thick. I suppose it couldn't hurt to try a shim (or doubled-up shim) of can or similar. "Mind you don't cut yourself, Mordecai."

Good point. The wedge is easily removed. Check it and see.

Those pics are spot on, thanks gents. I'll pull the bars out to check out the wedge next time I get a chance and I'm feeling ambitious. Thankfully it's not my only bike. It's a beautiful stem and an even more beautiful bike, I'd hate to have to change it out. It's probably the 26.0 in 26.4 because it's extremely close. I ride in the drops 95% of the time and it doesn't budge, only when I put a bunch of pressure on the hoods.

cleaned and lubed the bars? I never heard of lubing bars

Well it was creaking up a storm, I had to do something. Between the stem and the bar was logical.

^
Most handlebar creaks come from bars being sleeved rather than bulged at the clamp area. That said, a little grease never hurt anything, right?

Take the handlebar out of the stem and be sure that BOTH the wedge and the wedge nut are in correctly. They can be installed in such a way that the wedge moves forward, but not enough. Make sure they're in there the correct way.