hi there sandwhichmom!
Talk to them why they did that in the first place, usually children lie or commit dishonesty when they think that they will fail shoprt of your expectations, like when you expect them to have high grades, they will be forced to cheat or tell you they did good because they dont want you sad or displease. Tell them it is alright if they fall short at times. Explain to them that their behavior is not good and let them sign an agreement with you, (hold a paper with a pact on it) and let him/her write her name. The next time they will do that, it will be subtraction of stars, and everytime they are honest and tell the truth, you give stars to them in the contract. Then hug and kiss them, or give a high five.