Have a vintage bike and the bars will not tighten and appear to have a metal shim that extends to the bar tape on either end with some embossing and champion written on them. I don't want to over tighten the screw on the stem and ruin it. I just need it to not send me over the bars every time I brake. Am I missing something obvious here?

The shim is actually a sleeve that is part of the handlebars - very common type of construction in that era. What type of stem are you using? For example, if you are using a Cinelli stem (26.4 mm) with that Japanese Champion handlebar (25.4 mm), it certainly won't tighten enough.

I couldn't find any markings on it at all or I would have tried finding out what size bars it was meant to use. The bike is an 87 with all original parts that was kept in a basement for 24 years. It is a lower end bike which was why I didn't think it was a cinelli stem. I'm going to go measure the bars but is there a good way to identify the clamp size of the stem?

Other than measuring it? No.

The tenths of a mm measurement was going to be hard to measure accurately at the moment. Guess I'll start looking for a decent quill stem since I'd like it a little longer and some new bars to match. The step down from a dependable DA gruppo is serving as a good reminder how much more I like riding than wrenching. Thanks for the help guys.