In the sim, you'll see an error in the console. On a devices, you'll see it in \garmin\apps\logs\ciq_log.txt
Are you looking for some kind of automated way to find out about it, or have the app itself do something the next time it runs? I can't think of a way to do that.
What are you doing where there's a chance you may trigger the watchdog? It might be you can do things a bit differently and avoid the watchdog timer all together.
If you are doing something like sorting a large array, maybe a different algorithm, or something like building it sorted so you never have to sort the whole thing.
If your operation can trip the watchdog with certain parameters, I strongly suggest going with something simpler.
If you are close to tripping the watchdog, the performance of your watchface is going to be extremely sluggish, and will likely have a poor user experience. It is also possible it would have a noticeable impact on battery performance.
Another thing to note, is even if you cut back on things to avoid the watchdog on one device, it may not work on others, as the watchdog varies by device. You can look in devices.xml to see what it is on a device, and maybe plan/test for the device with the shortest one.