A "care miss" is required on the Pix, the Smart, and most older tamagotchi, in order to raise a specific character. The care miss method is:

When I do this, I keep a tally of care misses! I also run a timer once they call out my name, so I know for sure it’s been 15 minutes.

Note that on the Uni, if you feed the tama you have to wait an additional hour for the next Care Miss. So you may find it easier with the Uni to not feed the tama after the 15 mins are up. Just make sure to heal any sickness, and then wait for the next hour to pass without feeding.

This is also the best method for the Tamagotchi Friends and TamaGo.