I don't know the state laws that apply, but for the airliners:
1. Hard sided case with personal locks (not tsa approved).
2. Ammo in "crush proof" container anywhere in the checked baggage (loaded mags outside of firearm are OK, original box is OK, just not loose rounds. Ammo doesn't need to be in hard sided case with the gun)
3. Key or combo stays with you, and you only. (if they need it opened, you open it).
4. Declare at check in. Pay check baggage fee if any (ie: Delta $25 first bag, $35 second bag. If your first bag is over weight (50-71 lbs), split the checked baggage, otherwise it's $100 for an overweight bag. 71+ lbs is very expensive.)
5. Pick up at normal baggage claim.
Repeat process for trip home.
Last time I flew (04/12/2015 - 04/24/2015), to and from Salt Lake City, I had no issues. The TSA at Pasco WA had me open my case (49 lbs), which I found out later was because they just wanted to see my rifle, claiming it was too dense for the x ray. Just to hear, "I told you that's what it was," between two agents. They did have me put some airline tape over my mags to "ensure the bullets dont fall out." It was good, they ended up walking me through the express security line talking about firearms.
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