Reward vs Award

The correct verb to use really depends on the meaning of the corresponding noun.

Award (n): a recognition of a personal achievement, e.g. a scholarship for winning a science fair, a plaque for volunteering 100 hours of community service

Reward (n): compensation or incentive for doing something, e.g. cash for returning a lost wallet, getting to stay up late for tidying one's bedroom

The first sentence should be

My employer rewarded me with a trip to Hawaii.

The two verbs have a different meaning; to award suggests that the giver is in some sense a judge, and that the thing given is deserved (award a scholarship).