You can also contact the county court house where you were sworn in as an American citizen. It is part of the public record, and should not be hard for them to find... You can also contact the local library of the same county you were sworn in, if they do not have the record, they can point you in the right direction of where to look.
The citizenship and immigration service looks like the best place to ask. They have a form you can fill in to ask for records, or you might prefer to contact them direct and ask what to do. Alternatively, if you can remember where your certificate was issued, it could be quicker to contact that office first.
My husband is submitting form N-565 for replacement of his certificate of citizenship. The problem is he doesn't know the Certificate # & the A-#. Also he doesn't remember the exact month & day he was sworn. He only remembers the year. What can we do to find this information?