翠華龍=Green Chinese Dragon
褒章=medallion

As I could find only Japanese hits for this honor and nothing at the Shanghai Museum of Art, it appears to be an award especially designed to promote cross-cultural exchange. As the internet is filled with English language green dragon imagery in a wide variety of contexts, I find little wrong with translating the name of the award into English.

As the award appears to be issued by the Shanghai Museum of Art, you can probably leave out the reference to China when translating the name of the award. Just make sure that the Shanghai Museum of Art is mentioned as the source the award's source.

I do not believe that 龍華翠 is the name of an individual for if it were, the person would be famous and many Chinese hits would be found. Thus, there is no reason to rewrite it in latinized Chinese.

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Note added at 14 hrs (2006-05-24 00:08:12 GMT)
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Comment on NKWong's mention that 翠華龍 does not exist. As tokyoeditor may already be aware, Chinese, like Japanese, sometimes write from right to left in an effort to make -- what most contemporary East Asians would write from left to write -- appear traditional. A plausible explanation for mixing the order of the award's name and the word 褒賞 is preservation of the original Chinese, with a contemporary Japanese expression. By the way, the word 褒賞 can be translated in several different ways, as my entry above suggests.