I'm still a young learner of Japanese. However, I'm wondering what the approach of someone studying for one of the higher levels in Kanken would be. Particularly, the question where they give you a word in Katakana with a sentence for context. How would one study the homophones to be able to differentiate them?

You study them inside the context of the sentence in the same way the actual test questions are laid out. They are always inside a sentence or they always give you the context of a synonym or antonym to the word they're looking for. The test never asks for the production of kanji without also giving context. At higher levels of the test this context includes entire paragraphs while at lower levels it's just a very basic sentence.

The way I have my Kanji Kentei cards laid out is the same as the 書き取り and synonym/antonym questions on the test. You cloze-delete them, and leave the katakana pronunciation for the answer along with the appropriate context that should lead you to the right answer.

KanKen provides a full sample test for every level here:
http://www.kanken.or.jp/kanken/outline/d...ample.html

That was what I needed, thank you!