Look for legitimate affiliation. Legitimate poetry contests will be endorsed or funded by an official organization, such as the National Library of Poetry or a university or college. Be wary of contests that are privately funded or that don't list their sponsors openly. A contest without a major organization behind it could be a scam.
Locate past editions. Find previous winners and poems from past rounds of the contest. Legitimate contests should offer this information freely as an incentive to applicants. If you can't find an actual edition of poems or locate a past winner who can vouch for the contest, the contest might not be legitimate.
Find out how they found you. If you're invited to participate in a poetry contest via a random letter or email, contact the contest organizers and find out how they located your address and information. If your information was sold, you might have been included in a mass mailing list, and the contest might not be what it claims to be. But if there is a connection to a school or other writing contest or project you've participated in, this will give the contest more credibility.
Analyze the application. Misspelled words and improper grammar on the information pages and application are a big warning sign that the poetry contest is a scam. Legitimate poetry contest organizers should be masters of the language themselves. If the application is poorly written, that's probably because it's not the real thing.
Be careful when giving out your information. Poetry contests will require basic contact information, like email and mailing addresses, your age and some educational or personal information about your poetry background. Be wary of any contest application requiring detailed or sensitive information, like your social security number, credit card numbers, home phone number or any financial information.