A naturalization certificate helps you to prove that you have become a US citizen, with all the privileges of citizenship, including the right to live and work in the US, the right to re-enter the US if you have traveled abroad, the right to vote, and other rights as well. If you lose your naturalization certificate, you will need to file Form N-565 (Application for Replacement Naturalization/Citizenship Document) in order to get a new naturalization certificate from the USCIS. Depending on where you live, you will need to file your Form N-565 with either their USCIS Nebraska Service Center or the Texas Service Center. Form N-565 requires you to pay a $345 filing fee. In order to file the form, you will also need to submit photos that meet USCIS photo requirements and you will need to submit documentation to prove your citizenship status and identity.
Once you file USCIS Form N-565 (Application for Replacement Naturalization/Citizenship Document) to be issued a new naturalization certificate, it can take a year for your new certificate to get to you. In the meantime, you may need to use your US passport or other documentation to prove your status. If you do not have other documentation to prove your status, or if you need a naturalization certificate specifically before one year has passed, make an appointment with the USCIS through InfoPass. Bring as much documentation as you can; in some cases, the USCIS may be able to help you get temporary documentation to help you prove your status as a US citizen until your new naturalization certificate is sent to you.
Since it can take a year to be issued a new naturalization certificate, it can be a good idea to make a photocopy of your naturalization certificate when you receive it. In some cases, a quality photocopy of the certificate can be enough to prove your status. As well, you can use the information from the photocopy when applying for a replacement if you lose your original naturalization certificate.
If you are outside of the US when you lose your naturalization certificate, visit the closest US embassy or consulate, especially if you need your naturalization certificate to re-enter the US. However, do keep in mind that you will need to apply for a replacement naturalization certificate by submitting USCIS Form N-565 (Application for Replacement Naturalization/Citizenship Document) to a US USCIS office; you cannot file USCIS Form N-565 form abroad. You must also be willing to travel back to the US to pick up your naturalization certificate.