I've been stopped twice when carrying (once the weapon was on my person, once it was cased and under the seat). Both times I informed the officer immediately, and presented my permit along with my license (even though neither is required in my state). I had the permit & driver's license (along with insurance card & vehicle registration) visible in-hand before the officer approached the vehicle, with both hands on the steering wheel. I told the officer I was legally carrying a concealed firearm, and I was prepared to carefully follow his instructions. In both cases, the officer(s) asked where the weapon was, and I told them. They told me that it was fine where it was, just leave it there, and to keep my hands on the wheel, in plain sight.
We discussed the violations, and then they left to run my info through the patrol car's computer. When they got back, I was given a verbal warning (in both cases), and was released. I found it strange that in both cases, although they had clear evidence of a violation (minor speeding (5 over), and a lane change/passing violation), I was only given a warning. These were both city police officers, not state or county.
I keep my registration and insurance cards clipped to the visor, so I never have to dig through the glove-box to find them.
"Placement is power" -- seen in an article by Stephen A. Camp
(RIP, Mr. Camp; you will be remembered, and missed)