Preferred way to handle Java exceptions in ServletContextListener

For servlet lifecycle stuff, what do you guys recommend doing in response to an exception...

For example,

public class Foo implements ServletContextListener {

    @Override
    public void contextInitialized(ServletContextEvent event) {
        try {
           // something nasty
        } catch (Exception e) {
            throw new RuntimeException(e);
        }
    }

    @Override
    public void contextDestroyed(ServletContextEvent event) {
        try {
           // something nasty
        } catch (Exception e) {
            throw new RuntimeException(e);
        }
    }

I'm not entirely sure what will handle the runtime exception above. I'm working from the idea that if exceptions are thrown here, they're serious enough to break the system completely so an (unhandled) runtime exception may be ok.

I guess I'm asking what handles unchecked exceptions from servlet context listeners?