I often go with 2 rigs when I'm fishing, a 3 wt and a 6 wt. For me, I typically carry them both and set the other rod against a tree. For me, my rigs are normally dry rig on the 3wt and a nymph rig on the 6wt.

If I'm on a trip under a mile, I just carry the 2 rods rigged up normally. The rod not being used is leaned against a tree normally.

On my longer trips, I rig up my rods, but keep them in a rod case and attach the rod cases to my back pack, that also carries my lunch, water reservoir, rain gear, and depending on the length of the hike, may carry my wading gear (Depending on where I'm going).

During these longer trips, once I reach my fishing destination I'll typically get them both set up, if I plan on using them both. But most times, I only rig up one rod in these cases, as it's pretty clear to see which rod I need once I reach the water.