Personally if and when flying or travelling through customs or any form of officialdom I make sure ammo, even if reloaded is in factory boxes for the calibre and cartridge of rifle, and the brass and in particular the head stamp matches the writing on the box and on the rifle. I would also make sure the bullet looks similar to that on the box.
Customs officials look for discrepancies - that is within their DNA. Anything that is slightly out of order is of great interest to them. It either makes their day more interesting, or it gives an opportunity for additional fees, or both.
I have spent more days of my life than I would like in African customs posts at borders and in airports as well as police check points and road blocks.
Key is not to give them anything to start asking questions, as once they start, they will keep on going.
With anything Firearms related you are already volunteering to having things closely inspected. And if you have 458 Lott on the rifle, on your certificates, on your documents and yet you have 375 H&H on the cartridge cases, just make sure you are well lubricated for a thorough inspection. Why do you have 375 ammo when you permit says 458 Lott??
Trying to explain that you blow out the cases from 375 H&H to 458 to make the ammunition - ahh so you are making explosives then Bwana which is illegal. Why you doing this???
This may sound an extreme. Those of us who have lived and worked in Africa will totally empathise.
And given all the customs checks we now have here in the UK, getting stuff through customs will become an essential skill.