My limited experiences (pulled over once while carrying; waiting for police accident investigator once after a wreck where another driver hydroplanes and spun into my trailer) went along the lines of:
Me: (hand driver's license and concealed permit to the officer)
LEO: "Do you have it on you?"
Me: "Yes, sir, in a holster on my right. What would you like me to do?"
LEO: "Leave yours where it is, and I'll leave mine where it is."
Both were almost identically worded, one in Arkansas and one in Tennessee.
It probably helped that in both cases I was with my wife, and I am in my 40s with a military retired sticker on my truck, short hair, etc.