No standard 'Certificate of Freedom to Marry' document exists in the United States. You can however make a sworn affidavit testifying to your freedom to marry, which will be accepted in almost all countries.
In the past, the U.S. Embassy allowed American citizens to swear such an affidavit of eligibility to marry before a U.S. consular officer. The Embassy discontinued this practice several years ago, however, because local officials were interpreting these documents as meaning that the Embassy had actually verified the content of the citizens’ statements, when in fact the consular officer was merely attesting to the fact that the individual in question had made the statement.
You can find more information of a Legal Requirements for Getting Married in different countries on the web site Documents for Marriage Abroad

Prepare a standard Certificate of Freedom to Marry

Obtain an Apostille (for Hague Convention countries) or Embassy Legalization (for non-Hague countries)

Translate the Affidavit of Freedom to Marry into the target language

Have the Certificate of Freedom to Marry authenticated by the Consulate or Embassy of the target country