One of the ways to check if an email address really exists is to send the email and if the email bounces , it means that the email address does not exist. But there should be a better way to know this because if you send a test message , it would be delivered to the email address if it existed. There are other reasons as well to check the existence of email address. For one thing, you may want to purge your mail listing off non existing addresses. Secondly , you may want to be sure if you remember only part of the email address.
Etoolz is a free utility that does not require installation to work and verifies the existence of an email address. It does not work for all email services at the moment but surely it works for gmail right now.
Download the software from here. Initial language is set to German. Change it to the language of your choice from Extras > Sprache/Language . Run it and then switch to the Mail-Check tab . Fill in the parameters and click Start Button . The program returns if the sender and recipient are accepted . It will also tell you the reason that why the email would not be delivered. For example in case of email address being over quota.
There is one limitation of the program that it can not test multiple email accounts at the moment .