Your example may be translated as 彼女は[熱狂的]{ねっきょうてき}に歌った or something similar. This 熱狂的に with a particle-like ending に is actually an adverbial form of a na-adjective 熱狂的な, and is very properly translated as "enthusiastically".
Otherwise you can say it like 彼女は熱狂をもって歌った, where 熱狂をもって resembles "with enthusiasm" in appearance, with "with" being sometimes translated as をもって. However this kind of wording sounds fairly literary and less versatile, and is hardly heard in colloquial speech.