Another simple tactic that you can employ on antonym questions is to eliminate all answer choices that do not match the part of speech of the word in all capital letters. For example, if the word in all capital letters is an adjective, then the antonym must also be an adjective. Likewise, if the word in all capital letters is a verb, then the answer must also be a verb.
Why is this so? It's because the makers of the GRE claim that the answers to the antonym questions are precise, and hence making sure that the supplied word and answer are the same parts of speech is an attempt to stick to this practice. Consider the following antonym question:
Belittle means to scold, detract, or to diminish, and so belittle is a verb. Looking at the answer choices, note that choices 1, 3, and 5 are adjectives, and so they cannot be the answer. The fourth choice, value, can be a noun or a verb, and so we must leave it for consideration. Having eliminated all of those choices that are not verbs, we are left with just two! Downgrade means to lower, and is of negative connotation, and because belittle is also a negative word, downgrade is not a good antonym for belittle. This leaves only the word value, which, when used as a verb, implies proud ownership, and it is a positive word, which is in contrast to the word belittle, so value is the best antonym out of the word choices.