I hand them my permit along with my DL, although I am not required by Florida law to do so, and tell them that I just want to inform them so that they are comfortable and things go smoothly. On two occasions, the officers just asked me where the handgun was and told me to keep my hands on the wheel, then thanked me for the way I handled it at the end of the stop. On a third occasion, an officer made a snarky comment that the permit wasn't a license to commit traffic violations. I replied that I never expected it to be, and repeated my reasons for informing them. Another officer took Officer Snark aside and spoke to him for a few minutes, then at the end of the stop (for a burned-out tail light that I didn't know about) told me that I had handled things well, and thanked me.
I always thought that if I was an LEO I would appreciate folks being up front with me about the presence of a firearm, and LEOs who post on these boards often say that is their preference, so I go beyond what is required by law. That isn't everyone's choice, but it is the way I have handled it, so far with success.