A cup of green tea contains about 25-30 mg of caffeine. The tea bags contain a lot more caffeine. However, when it comes to caffeine, green tea may offer the best solution to that caffeine dilemma. Black tea has about 40 mg, and drip coffee with its 90-150 mg. can keep you up all night. Fortunately for the tea lover, green tea also contains theanine, an amino acid that functions as a natural tranquilizer so the caffeine does not pack such a wallop if you’re trying to sleep at night.