While the existence of these ceremonies seems diametrically opposed to the American way of handling a divorce (parodied here by Indigo Productions), the thinking is to provide a symbolic ending so that both the husband and the wife can move on to the next stage of their lives.
In Massachusetts, the closest thing to a divorce ceremony that we have is the uncontested divorce hearing. Very different from a trial, the uncontested divorce hearing occurs when both parties agree to the divorce and have reached an agreement on all outstanding issues. After a short approximately 10-15 minute hearing in which the Judge reviews the agreement and a basic case is entered into the record, the Judge declares that the parties have demonstrated sufficient facts to obtain a divorce and that a Judgment of Divorce Nisi will be granted thirty days after the hearing. Ninety days after that, an absolute Judgment of Divorce is entered and the couple is officially divorced. Basically, it takes four months of waiting from the last date that you go to court before you are technically divorced. How unceremonial.