The pressure that can be felt when running an event has much to do with the word itself; event. An event is a moment in time, and it has to run right at that time. In other areas of business you can come back tomorrow and fix a problem. It may not be ideal, but if you are fitting a window and need to come back to sort something out you can still end up with a happy client. That is not the case with events.
There is no doubt that stress is contagious. If key people, for example the Event Manager, are showing signs of stress then other will start to feel it too and mistakes will be made. The Event Manager needs to seem to be in complete control, even if he or she is paddling fast under the waterline. The most stressful time is just before the event gets underway. Once things are starting to happen then everything changes and you can focus on delivering what has been planned.
Another role of the Event Manager is to take the pressure off the client, so they can enjoy the event with their colleagues. This is not always easy, and clients very in their need to be hands on. One of the most challenging situations is the client who is watching everything and checking things off a list. Good Event Managers are experts at filling in and maintaining their cool. Often things will not go quite to plan, but with the expert handling of a professional no-one will notice ... unless you have a micromanagement situation. It is much better to trust the Event Manager to make things work.
This really comes down to trust and this is something that is built before the event. Trust is hard to build and easily destroyed, and being calm in the face of pressure is absolutely vital.