I copied this idea from another instructor at our school and then modified it to fit the content of my classes. I attach a coupon to the end of my residential class syllabus addenda that allows each student one late assignment. There are several conditions and exceptions (not good for quizzes, exams, in-class assignments, etc. and must be handed in the next class period, etc.). Students who don't use it receive one to two bonus points on the final exam. I make the coupon look kind of cheesey and use all sorts of infomercial-type phrases (I teach marketing). They can use their coupon regardless of the reason. This takes a lot of the judging responsibility off of me and lets students know that I know that "life happens".