PA.
These ( diversions, emergencies, delays , technical return to bay etc) are perfect examples of testing a captain's management skills and can be the difference between an inconvenienced ,manageable passenger and a disruptive, aggressive passenger.
The Public address(PA) is more than a hello / thank you announcement . It is a major tool in calming the frayed nerves of your passengers. An honest, open PA explaining the situation in as simple terms as you can explaining the technical/ safety ramifications of the delay keeping in mind the average understanding of the terms and truly being sorry for the inconvenience they(PAX) have to undergo goes a long way and believe me, ask your Cabin crew what they think about your PA.
It has made the difference many a time in my personal experience over the diversions, delays and technical turn-backs that I have done. Understand your passenger demographic , know how they think and what they understand , try communicating with them than just talking at them. You will still get the odd resentful/obnoxious one but it's more a grumble than a collective revolution in the back .
Indian fliers are difficult to deal with, you'll have a first flight passenger who has no clue about the rules/etiquette of flying seated next to the high flying business tycoon who flies business class all around the world to the classic grumblers etc. But the challenge of being a good captain is to fly safely and also find time to address your passengers and convey the message across thoughtfully . I once had a lady telling the crew ," The captain is lying , my cousin says there's no fog in &^%$pur" , yes maybe not at his home , but the airport is 25 kms away in the middle of nowhere duh. But, no use getting angry or flustered , get on with the job of communicating regardless.....
Now, that said, what we also need is support from the airline once we get back to parking at the bay. A good airline is ready with a plan before the aircraft gets on the bay, immediately addresses the needs of passengers (missed connections, offloading,refreshments etc.) and co-ordinates well with the captain and other agencies to get the aircraft back in the air. I've been lucky to have the support of the excellent ground staff of Jet Airways( I work for their subsidiary) all over the country but the same might not be the case of Air India.
These instances damage the airline's reputation and winning back the trust of your passenger is very difficult , therefore the great need for all parties concerned ( Pilots, cabin crew, ground staff,management) to be working together to cater to the needs of your salary-givers( passengers).
Happy flying and masalama.