There are three resources I would look through. Writer's Digest - their different market guides (Poet's Market for example) list contests as well as a big section on different publishing markets. They will list info about costs and so on. The market guides are published every year. Poets & Writers I believe also lists contests. You can check their website for free. Duotrope lists marketing information for journals, book publishers, and contests. You may need to do a bit of playing around with the search for what you want, but the Calendar lists upcoming deadlines which may be helpful.
In ALL cases, look at the publisher/contest holder website. You need to use your own discretion when checking them out. If something sounds too good to be true, it probably is. One thing to note is that a lot of contests are run by universities and probably have been running for a long time. IMO those should be safe. Contests often charge fees, so take that into account - the amount may vary.