Depending upon the stat you live in and it’s legal requirements you may or may not need witnesses to sign your license. Just to clarify on one point, there is a difference between the license and the certificate.
In NH the license is just that – a ‘permission’ to marry. This document will inform the officiant that you have presented the necessary paperwork to a clerk and they have verified that you meet the criteria needed to be joined in a legal marriage. Once you obtain that license [and wait the 3 days where needed] you can choose your officiant and the style of wedding. If you are having a big formal wedding, all that will have been done prior to obtaining the license. Don’t forget that no license means it’s not a wedding, it’s just a commitment ceremony.
The marriage certificate is a document that certifies that the license was issued, completed and filed as a legal proof that a wedding ceremony was performed and you are now legally married. the certificate will be issued by the clerks office that issued the license. The officiant files the paperwork in NH and also many other states. It is then your responsibility to obtain the certificate from the clerk to use as your proof of marriage.
In other states you are required to have two or more people sign the license as witnesses to the fact that the ceremony took place and the commitment was made to be legally wed. I have performed weddings in both Maine and Rhode Island, and both had this requirement. In such cases I like to have the witnesses nominated prior to the ceremony, and where possible the signing included as part of the ceremony. It is totally up to the couple how they would like to have that done.
If you are a witness, your task is simple. Attend the ceremony, witness the vow taking, sign the form. After that, the officiant will file it with the clerk and the certificate will be ready in approximately two weeks, depending upon the office. There is a fee to obtain the certificates to cover their costs.