In Spanish (at least in Spain, for other Spanish-speaking countries like Venezuela my opinion is less relevant) we would not say “ceremonia o servicio prestado” (“prestar” just sounds wrong), but instead “ceremonia oficiada por” (“servicio” also sounds a bit weird in this context). I assume the wedding ceremony has been a religious, not a civil one. That´s why I suppose that the officiant is a clergyman and he has solemnized it.

If the “minister” is then a “minister of God” (= priest), what I suppose, we need to specify this key aspect in the translation.

If I am right, I would avoid the expression “ministro”, which sounds to me a political, not a religious position. In European Spanish, “ministro de Dios/del Señor” could be possible, but sounds very strange and is extremely old-fashioned.

This link describes in detail the people authorized to solemnize a marriage in New Jersey. In my understanding, a “minister” is here a “minister of God”, i.e. a priest, a clergyman.
http://www.ordainmeplease.com/Wedding_Officiant_Laws.html
Wedding Officiant Laws by State
New Jersey
In a nutshell: Any ordained or licensed clergymen, and justices of the peace.
37:1-13 Authorization to solemnize marriages 37:1-13. Each judge of the United States Court of Appeals for the Third Circuit, each judge of a federal district court, United States magistrate, judge of a municipal court, judge of the Superior Court, judge of a tax court, retired judge of the Superior Court or Tax Court, or judge of the Superior Court or Tax Court, the former County Court, the former County Juvenile and Domestic Relations Court, or the former County District Court who has resigned in good standing, surrogate of any county, county clerk and any mayor or the deputy mayor when authorized by the mayor, or chairman of any township committee or village president of this State, and every minister of every religion, are hereby authorized to solemnize marriage between such persons as may lawfully enter into the matrimonial relation; and every religious society, institution or organization in this State may join together in marriage such persons according to the rules and customs of the society, institution or organization.
Marriage License Requirements Link: New Jersey


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Note added at 1 hr (2013-06-24 17:37:32 GMT)
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This is applicable to Colorado:
http://www.abargainminister.com/justice-vice-minister.htm
The Difference Between a Justice of the Peace and a Minister
Justice of the peace is another name for a county judge. To be married by a county judge, you have to go to the court house where the judge presides, usually in the county seat, make an appointment with a judge, buy a marriage license (currently $30 in Denver and surrounding counties), and show up when you’re told to. The “ceremony” takes place in the judge’s chamber, or office, where he or she recites a short, canned script before pronouncing you married.

Typically ministers are ordained by churches. Different churches have different criteria for ordination. Most require a course of study, usually at a divinity school or seminary. People calling themselves “non-denominational” ministers may have sent money to the entity that calls itself the Universal Life Church. This church then sends them a certificate of ordination, making them mail order ministers. That doesn’t mean they don’t do a decent job of officiating, just that their ministerial credential is shaky.



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Note added at 15 hrs (2013-06-25 07:34:38 GMT)
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Have found this on the Wikipedia:
http://es.wikipedia.org/wiki/Ministro_religioso
Ministro religioso
Ministro es el título dado a individuos en diferentes iglesias cristianas y que varía dependiendo de las mismas.
(...)
En la mayoría de las iglesias protestantes, un ministro es un miembro del clero ordenado que lidera una congregación; tal persona puede también ser llamada pastor, predicador, anciano, etc., dependiendo de factores como las tradiciones, usos y otros. En muchas iglesias, se requiere que los ministros hayan sido educados en seminarios, pero algunas iglesias permiten que los laicos prediquen.

The title of the Spanish article says it all. "Ministro" alone is fully confusing in Spanish, should be avoided as a translation, IMO. "Ministro religioso" would do if you don´t know if the person in question is a ordained Member of the Anglican, Catholic Church, etc., etc.

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Note added at 15 hrs (2013-06-25 07:35:49 GMT)
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Sorry, I meant "aN ordained member (...)".