This sentence is from my essay. Is the semi-colon correct?
His most famous residence is the Kaufmann Residence; esteemed for its use of organic architecture with Japanese architectural components to create harmony with the residence and nature.
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No, I'm afraid you need to replace it with a comma or recast the sentence (I would choose the latter). You'd normally only use a semicolon if the part that comes after is an independent sentence. This is not one of the typical exceptions.
The general construction your sample exemplifies, in learned written English, is:
[Clause establishing topic], [Comment on topic]
In this case, the topic is "the Kaufmann Residence," and you have a comment consisting of an adjective phrase ("esteemed for..."). The comment need not be a full clause. Another example, from a piece of fiction occurring in the New Yorker:
She had a room on the side of a house, wobbly wooden stairs leading up.
When you use a semicolon to separate a topic-establishing clause and a comment, the comment must consist of a full clause. That is why it looks bad as it is.