Delegate your responsibilities. Everyone finds themselves with too many obligations on the horizon. Choose to attend the most important one yourself while sending a trusted stand-in to represent your position at the other appointment.
Use video conferencing. Science does allow us to transcend time and space, to virtually be in two places simultaneously. Professors and corporate trainers use this technology to teach two classes at once, even when the classrooms are physically halfway across the world.
Pay someone to appear on your behalf. Lawyers are one group of people who make careers out of speaking and acting for clients that are not physically present. Waiting in line to be the first to buy the latest electronic gadget; purchase the services of a temporary place-holder or line-holder.
Meditate your way to another place. All joking aside, meditation is known as a practice that helps calm the mind and body while producing lasting health benefits. Traveling mentally is a great stress reliever.