For travel outside of the U.S., the airline will print a telex of your message for delivery at the arrival or connecting airport gate.

Inside the U.S. things are less easy. If the traveler will be using an airline lounge, contact the lounge staff (the airline can direct you to their actual phone number). Another option is to notify the police in the arrival city (assuming this is something of that level of urgency) and ask them to await the arrival at the gate.