Yeah, if you need quickly, get a levergun.
Seriously, I use:
1. Shirt with sewn-in cartridge pockets above the left shirt pocket, 2 of them for 2 rounds, with suede collars to grip but not bind. One shirt holds .30-06 size, the other holds .375 H&H.
2. Westley Richards cartridge wallet on the belt holds 4 rounds.
3. Trapdoor cartridge holder in the comb of the buttstock holds 4 rounds.