Sorry to gravedig but this is one of the first posts that comes up in Google when searching for how to check your Pasmo balance online, so I thought I'd post a solution for anyone else who comes across this post first.
If your phone supports the NFC function then you can install an app which allows you to check your balance by pressing your card against the back of your phone. There are a variety of apps available, some in English and most in Japanese, and most are free. I installed one called Suica Reader. After installing I just pressed my card against the back of my phone and it displayed my current balance and history of use. The details in the history are all in Japanese but the current balance and the user interface are all in English. Despite the name the app works for both Pasmo and Suica cards which both apparently use the same system.