I put new Bridgestone Potenza tires on my 2005 CTS and I have a vibration when traveling 55 - 65 mph. I have had the tires balanced and rebalanced three times. I recently installed new brakes and had the rotors machined about 1500 miles ago. Also, when braking off the freeway, I get a big vibration from the brakes from the same side that the vibration at 55-65 comes from.
A loose wheel bearing or suspension component such as a tie rod, tie rod end, ball joint, etc. could cause a vibration and even mimic a brake shudder.
A dragging brake pad on the brake rotor due to a brake caliper problem or the caliper sticking on the caliper slides could also cause this.
If it was not done, the caliper slides should have been serviced during the brake job.
It’s also possible that the tire balancing machine could be out of calibration, although most of the time that would have nothing to do with the brake shudder.
You need to find someone with a Hunter GSP9700 Road Force Balancing machine. That machine will 99% of the time find the offending tire or wheel component - if there is one.
Unfortunately, your vehicle is one of the most sensistive vehicles ever made. The technician operating the Hunter machine needs to be looking for values below 10#.
Hopefully that will fix the problem. If not post back.
In addition to the excellent advice given by ok4450 and CapriRacer, I want to add that you may have made a tactical error by having the brake rotors machined, rather than simply replacing them for a few bucks more. Machined rotors are thinner than original specs, and thus are more prone to warping than originally.
If Road Force Balancing does not resolve the braking vibration as well as the vibration that you feel when driving, then you need to have the front end examined for loose, worn, or damaged components. If all of this does not help, then you just may have to replace the rotors in order to get rid of braking vibration.
I’d say one of your new tires is defective. If a tire has a bad belt it can balance but still not run true. Braking forces can accentuate the fault.