i have a cousin who is going to El Salvador this winter to marry his fiance, would the USA recognize his marriage?

Generally speaking, yes. See here for more information.

There is no special procedure or authority solely empowered to recognize marriages entered into abroad. The question of whether a marriage is valid is therefore always only a preliminary issue in connection with other administrative acts (e.g. change of name, application to start a family book at a domestic registry, change of entry on one's tax card, etc). This preliminary issue must be determined by the agency responsible at its own discretion.

The basic rule is that a marriage entered into abroad will be regarded as valid in Germany if the legal provisions relating to marriage of that foreign state were abided by. In addition both the bride and groom must meet all legal capacity requirements for marriage under the law of their home states (they must for example be single, over a minimum age and not too closely related to one another).

A foreign marriage certificate proves that a marriage has been entered into abroad. In some states (e.g. the US and Canada) the couple is only given a provisional certificate (or a "summary marriage certificate") after the ceremony. The marriage must subsequently be registered with the competent authority in order to obtain a full extract from the register. For further information see the fact sheets produced by the Federal Office of Administration (see "Legal provisions relating to marriage" below).

Foreign marriage certificates are often only recognized by domestic authorities or courts when their authenticity or evidentiary value has been determined in a separate procedure. A range of standard international procedures have been developed, which you can find out more about under the heading "International Recognition/Legalization of documents".

This page may be useful for anyone wishing to "see "Legal provisions relating to marriage" below" or wondering where the "heading "International Recognition/Legalization of documents"" is, although I'm not sure how useful marraige laws in Germany are to the question of whether a marriage in El Salvador would be recognized in the US.