Originally Posted by paramour
This is what I do as well. Students are informed that if they miss an exam for any reason whatsover (e.g., illness, flat tire, failed alarm clock, tornado stole your vehicle, blizzard, excessive partying, golf tournament, the petsitter canceled, alien landing, the latest apocalypse, etc.), then they are allowed to take the make-up exam on the final day of class (which also happens to be the day scheduled for final exams--I dropped the final exam in this class in exchange for a semester project, so no need to worry about multiple exams unless they missed multiple tests). Documentation not required. Students are forewarned that questions may be more difficult than the ones on the original exam and/or in another format, so they really shouldn't make a habit of being absent. If they miss the make-up day, then too bad. They are not given a second opportunity.
Our program actually prohibited this, as it was seen as penalizing students who had valid excuses. Thus, the make-up couldn't be substantively more difficult than the original exam; you definitely could change the format from multiple-choice to short answer or essay, though.
Agreed with the others, though, that a clear statement up front/at the beginning of the semester (and frequent reminders throughout) is the best way to avoid most problems. I actually had a fairly lenient make-up policy, and I think only ended up having to administer maybe five over two semesters.