Lost certificate of Citizenship?

You've been given the solution.

If you want a legal copy of the certificate, you'll have to pay.

You can't get a passport without the certificate.

The day after you got your Certificate of Citizenship or Certificate of Naturalization you go to the passport office and apply for a US passport. Why?

Because you want to avoid having to apply for a certified copy of the certificate. Not so much because of the money, but because it can take over a year to get it.

The day after my naturalization I went to the SSA office and was there before they opened the doors, and updated my records with them. I was out of the office 12 minutes later and drove straight to the nearest passport office. I couldn't sleep all night being afraid that something could happen to my Certificate and I'd have to prove that I"m not an illegal alien.

This is why all those State Dept. workers with clipboards were walking around at your oath ceremony. Applying for a passport at the time of naturalization is a lot cheaper than what you're going to have to do now. 

First, are you asking about a certificate of citizenship or a certificate of naturalization? 

You get a certificate of citizenship when you actually obtained US citizenship at birth through a parent who didn't register your birth before your 18th birthday. 

You get a certificate of naturalization when you obtain US citizenship after emigrating to the USA.   

An OFFICIAL birth certificate will work.