A self-uniting marriage is one in which the couple are married without the presence of a third-party officiant. Although non-denominational, this method of getting married is sometimes referred to as a "Quaker Marriage".
Although most states do not offer self-uniting marriage as an official option, Pennsylvania has recognized such marriages for centuries (due to its Quaker origins and history of religious tolerance) and has offered licenses for these marriages for decades. These marriages only require the signatures of two witnesses in place of an officiant.
The issuance of self-uniting marriage licenses is controversial, however. Some Pennsylvania counties do not offer this form of license at all. Others only allowed such marriages when license applicants could prove they were members of a recognized religion without clergy, such as Quakers, the Amish, and the Bahá'í faith; however, in 2007, a Federal judge ruled that a Pennsylvania couple that was denied a self-uniting marriage on the basis of their secular beliefs must be allowed such a license.
Wisconsin also allows self-uniting marriages, without asking questions, but a form must be signed that states that the government issuing the marriage license cannot guarantee that the marriage will be recognized in all contexts.
Colorado allows self-solemnization without requiring a special form of application or witnesses.
The District of Columbia also allows couples to officiate their own wedding. 
- U.S. District Court for the Western District of Pennsylvania Temporary Restraining Order, Knelly v. Wagner
- Ward, Paula Reed (September 22, 2007). "Couple fighting for rights over rites". Pittsburgh Post-Gazette. Retrieved July 26, 2011. "However, officials [in Butler county] said they don't issue that type of license at all"
- Knelly v. Wagner, Federal Court, Western District. http://aclupa.org/legal/legaldocket/couplerefusedselfunitingma
- Ward, Paula Reed (September 28, 2007). "Judge says couple can have self-uniting marriage". Pittsburgh Post-Gazette. Retrieved July 26, 2011.
- 14-2-109. Solemnization and registration, Colorado Revised Statues, "A marriage may be solemnized... by the parties to the marriage...."
- DC Courts: Information on Marriage, retrieved May 12, 2014, "Pursuant to the "Marriage Officiant Amendment Act of 2013", the following persons or organizations are authorized or are candidates for authorization to perform marriages in the District of Columbia:... (9) the parties to the marriage (both parties to the marriage must apply in person with a vaild government issued identification)."