I also missed my flight in Japan. It wasn't a big deal. I took a bus from Narita to Haneda, asked if there was another flight there, there wasn't, so I just stayed there for 3 hours to charge my phone. Then I took another train back to the city, just to have breakfast. Basically I just toured the city again to pass the time. Then went to Narita airport again, and I was able to get the same flight that I missed the day before, I just had to pay $100 extra or something.
There's one flight per day, so if you miss the flight, you can just wait 24 hours, and take the flight the next day.
The only bad thing is that I wasn't able to take a shower, so hopefully I wasn't too stinky by the end of it.