When it's really, really important to be there, send it FedEx

, or travel a day early. Because things happen. Weather, mehcanical breakdowns, strikes, overbookings, lost baggage, and much more than I can begin to name.
And be prepared with alternate flights information, help desk telephone numbers, etc. to make it easier to get things fixed. Even carry a "Conditions of Carriage" or other relevant rules with you. Most important, deploy an attitude that makes you easier to help than others, to ignore you or even retaliate agianst you. When traveling, think strategically.
These relatively small changes to travel plans have saved my bacon a number of times over the years. No measure of high technology and aircraft improvement have changed the fact that "things happen".