As others here have noted, proving cheating via technical means can be difficult, if not impossible in some situations.
I've found that a surprising amount of people buckle under pressure and admit to cheating or dishonesty if you simply (gently, but firmly) ask them if any cheating took place. This is especially true if you ask with a kind of calm confidence that says "I know something happened."
Do not throw accusations, show aggression, or insinuate anything. Simply ask an easy-to-answer question or two and take it from there. If they do not admit to anything, call it a day and move on.