You have to ask your customers to confirm their email address, i.e. entering it twice to reduce misspellings, asking to register and sending an activation link and so on. State explicitly they need a valid email address: if they're asking you a quote why should they enter an invalid address? But be aware some people may use disposable email addresses to protect their real ones.
You have no way to check if an address really exists just asking its server. Due to the large amount of spam and techniques implemented by spammer to harvest and clean their addresses lists, most servers are setup to defend themselves.
That's why I suggested to "be polite". I am sorry if you got it the wrong way, I was just telling you that if your application shows a "spammer-like" behaviour (and your previous version of the question was much unclearer about your aims), it can lead to your IPs being blacklisted. Then you can have much more troubles to send quotes to customers.