When the unexpected arises, I believe there are a few strategies that will help no matter how serious the problem is.
First you can only focus on what you can control. Worrying about what you can't control is unproductive. In times like these the one thing you should be able to control is your state of mind. You will need to stay calm, because as the leader people will look to you as the rock they can lean on. If you are panicking and unsure of yourself, this will send a negative message to those around you, who will then start to panic themselves.
The other mind set to adopt is one of a positive nature. It is incredible what can be accomplished when you are in a positive state of mind. Staying positive will give you the strength and optimistic outlook that the crisis will be resolved, and you will be more likely to search for the solution.
As you search for what to do it may mean you have to make decisions on the spot, especially in times of an immediate crisis. Since there is no policy in the matter, you will have to use your experiences and training to do what is best. You do have to think about the effects that your choices may cause, and having a few trusted individuals that you can bounce those ideas off of, can be a great asset.
Another choice I would make is to be transparent. I would not hide information or my feelings. I would just be in control of them. When people see you as honest and upfront, I think they will respect you more. If you have their respect then being their leader is half complete. I think it would be very difficult to lead anybody if you did not have their respect. This respect is something that will have to be nurtured and developed before any crisis, but to keep that respect you must be able to lead during a crises.
Being prepared is also key. This makes me think of how pilots train in simulations for any event. It most likely will never happen to them, but they are prepared for that unlikely chance of mayday. We as leaders need to prepare our minds by learning from others, reflecting, and thinking how will we act in certain situations. Playing this out in our mind and visualizing is a good way of simulating any crisis before it happens.
It's how you think first then act that will help you lead during a crisis. You need to understand the situation, the community, and the times you live in. It starts with you and your state of mind. If you have control of this, and are prepared mentally, you increase your chances of being an effective leader during a crisis.
Ultimately those crisis you encounter will help shape you as you learn to get thorough them and how you get through the problems will help define you as the leader you are.