The key to knowing when to use whom versus who is knowing whether the pronoun is the subject of the sentence or the object of the sentence. The subject of the sentence is the noun doing something in the sentence; the object of the sentence is acted upon by the subject.
Consider the following sentence:
She hates Brussels sprouts.
In this sentence "She" is the subject, "hates" is the verb, and "Brussels sprouts" is the object. The subject (she) is acting (hating) on the object (Brussels sprouts).
A quicker way to know whether whom or who is correct in a given sentence is to figure out if you can replace the word with either him/her or he/she. If it's the former, the correct pronoun is whom; if it's the latter, the correct pronoun is who.
Consider this sentence:
Who/whom was there?
"Him was there?" and "Her was there?" make no sense, but "She was there?" and "He was there?" do. So who is correct here.
Looking at your sentences, the one that correctly uses whom is the second one - To whom was the award given?