My question is about USA, I have booked a flight from BDL (Bradley International) to Miami with one stopover. A week later I found a better (non stop) cheaper flight. Is there a trick, like price match, etc?
Once you bought it, you are pretty much stuck with it. Some airlines offer a 24 hour grace period for canceling or re-booking, but a week later you are out of luck.
If your ticket's fare rules allow changes, you might be able to get the better (non-stop) flight, but the change fees will wipe out any fare difference and probably end up costing you more.
You ever heard of 'Rule of Acquisition #5'?
Once you have their money, you never give it back.
That applies here too, but: 'non-refundable' does not necessarily mean 'lost' - most airlines allow to cancel or change the flight, and the price gets 'stored' with them for up to twelve months (counting from the day you bought the ticket, not when you canceled). Within that time, you can use that 'stored' amount to buy another ticket; however, there will be a fee for the change, which is - depending on airline - anywhere between 0 $ to 400 $, or even more. So a) that might not help you much, and b) it might be a larger loss than your gain, but still, it might be an option.
Judging by its name, a non-refundable ticket is as non-flexible as you can get it, though nothing can be certain without seeing terms and conditions. I doubt there would be a price match incentive (what's the benefit for the airlines?)
However, I advise you to call and ask if it's possible to cancel. Airlines often overbook, and if several people with a flex ticket have rebooked seats on your flight, the airline may actually want someone to cancel now to avoid bumping people at the gate. Most probably your request will be turned down, but nothing prevents you from trying.
You have to check your fare rule, afterwards if is convenient for you can ask for a partial refund and buy the new ticket.
Usually if is not a full fare penalty, it will cost you about 100 $ / 180 $, anyway could be higher.
If you provide me you departing and arrival airports, and just the fare basis of your fare I can get the exact penalty amount for you.