I dealt with this a few times in MI, and it was no big deal, because there's a requirement to inform the officer. Just told them to keep their hands where I could see them and that was that. Never had anyone NOT inform me, but I could see getting a little crusty with someone if I saw it and they didn't tell me it was there.
Now that I'm in IL, it's a different story, since there's no CCW (but that will change shortly, which I really couldn't care less about). The only time I've run into an "issue" was stopping a guy for 50/35 a few weeks back.
I never would've known there was anything in the car, except that he just stops looking for his insurance and says, "it's in the center console." I said that's fine, and he responded, "well, there's 2 guns in there." I asked if they were loaded, he said no, I asked why they were there, he said the center console constitutes a case in IL, according to a recent change in the law.
I asked him to step out so I could retrieve the insurance card, he did so. I inspected the guns to ensure they were unloaded, checked with my W/C on the legality of him having them, found out he was right, checked his FOID status, wrote him his warning, and he was on his way. Even shook his hand and said thank you for teaching me something. We even laughed that in a few months, it'll be a moot point, since he might be able to carry it on his hip.
All in all, that's about the best way I feel it could go. He wasn't a jerk, and had he not had to go into that console, I never would have asked him out of the car.
The name on the left side of your chest represents who you work for. The name on the right side of your chest represents who raised you. Make them both proud.