I second the "refill meds early" plan ...have been doing that for years and have several stashes of xtra meds (rotated of course).
Containers used vary ...and your pill requirements affect your choices too. Some pills are smaller than others and stashing 30 days worth is clearly easier with smaller pills.
I never travel without at least a 30 day supply...and have a weeks worth on my key chain and another in my desk at work.
In addition each first aid kit has a stash...and the little personal sized one I keep in my luggage has a separate stash than the one in my shaving kit.
Like reading glasses ...I tend to "salt" them around in the hopes at least one will be at hand when I need it.