We have to keep our phones with us - for work and/or pet-sitter access, but also for quick access to MDE if we want to check or change plans.
I carry mine in a tiny crossbody purse that is small enough not to have to be removed on any attractions -- or even at restaurants or in restrooms, ensuring I can't lose it! (I keep a Ziploc sandwich bag in the purse as well, to toss the phone in when I go on wet rides).
DH wears longish, Bermuda-style cargo shorts (fashion police, don't you dare say a word - my man makes those shorts look GOOOOD) and puts his phone in a side pocket that has a zipper closure so it can't fall out. Because that puts the phone essentially next to his thigh rather than at his waist or on his hip, it's never in danger of getting damaged by any ride restraint system, either.