Earlier quoted context omitted.
I realize that I am not typical, but I seldom even have my phone turned on, and don't even take it with me very often. I was tethered to a phone for years. I am retired. I only take it if I am expecting to be idle. Then, I take it so I can browse while waiting. It feels kinda nice, frankly. I am not a technophobe. It's just nice to not be beholden to my phone.
This reminds me of my experience giving up my wristwatch. I would glance at it frequently, but then didn't know the time because the behavior was strictly reflex. Finally, someone asked me for the time right after I did this and I had to look again because I hadn't internalized it. That was the day I removed my watch forever. Your comment about being beholden to your phone reminds me a a great quote that I recalled o…
Later on, maybe by 2010, I had noticed that as my aversion to blackberry vibrations emerged, and I avoided my work-related cellphone more and more, I got really good at ballparking the time to within a margin of maybe two minutes, give or take.
Basically by now, somehow, I'm able to glance at a known clock with an accurate reading (or with a known offset to the accurate time), catch the time once, and usually remain pretty accurate for the next handful of hours, until I get stuck in a sufficiently distracting situation that demands concentration. Up until that point, I try to guess the time to the minute before looking, then look, and often, I'm right on.
I don't have any special method beyond that though. It's just a gut feeling I've accidentally developed. I think it started when I disabled rings and vibrations for email alerts and I'd (with an amount of dread) try to guestimate how many emails would drop before the next time I checked my phone, and the minutes since my last look.
I think the next level up, beyond this skill is memorizing relevant time zones and major cities in each, but I haven't been pushed into caring about something like that quite yet.