As a DM in an RPOL 5e game, I've found it tough to figure out how and when to award inspiration.

Maybe it is just my players, but they are all good at inhabiting their characters and writing in interesting ways. If I award it for good role playing, all of them would have inspiration pretty much all the time.

I wonder how other 5e DMs are dealing with inspiration either here or face-to-face.

Face to Face is a little easier, since players in real life games don't have hours to deliberate what they are going to say. IRL D&D its more of a in the moment roleplaying so I at least see a difference in dialogue compared to play by post.

Haven't played any 5e on here, but if it were me, I would do it based off actions that are selfless.

Stick to the script. Interesting writing shouldn't be the standard - Award inspiration for making tough choices; choices that illustrate the character even when they aren't the best game choices to make.

Does the impulsive rogue argue for the go-charge-now approach, even when the character is more effective with careful planning and execution? Inspiration.
Does the over-confident Paladin recommend resting to recover spent resources? I don't care if his eloquent, evocative prose could talk Cicero out of his toga, no Inspiration

Does the young Squire call out the Champion of the Realm for insulting his Lady's honor? Inspiration - even if he misspells most of his words.