TL;DR If your sequence is 29.94fps, trying copying and pasting your sequence into a new 30pfs. Export as H264.
While trying to airdrop a 1 minute clip, I repeatedly received the message:
Airdrop can be fussy. I'm not alone, so yes other people are trying to figure this out too, but I also don't want to watch a 10 minute video on how to fix it.
So here's my answer: the native format for my camera is 29.97fps, and I think iPhones "like" 30fps. (I think they can play all sort of formats- Filmic Pro can record at 24fps and the iPhone handles this fine.)
I had no luck importing this 29.97 QT clip into Quicktime Player then re-exporting. One alternative solution was to create a new sequence in Premiere that is H264 and 30fps instead of 29.97. Then drop the existing sequence into that new sequence, forcing it to conform to the adjusted rate. Then try making another export using H264 format, and use 'Match Source' as a preset. This file was 84mb, and went to the iPhone via airdrop without any other conversion hassles.
Good luck.