I have a policy (that I explicitly put in my syllabus) that I will give make-up exams for "emergencies". However, make-up exams consist only of essay questions & are often a bit longer and harder than the regularly scheduled exam. This technique is effective in my lower level courses that traditionally have exams that contain a mixture of multiple-choice & short answer questions. I've found that most students will do anything to avoid the essay exams, if at all possible.
Lisa Harrison, Ph.D. Department of Psychology California State University, Sacramento