Azamara is not designed as a ship for families. Even though our cruise was in the middle of summer holidays for Europe, we only saw a handful of kids. While the line's destination-immersion focus may appeal to history- and culture-minded teenagers, they should be prepared to make their own fun.
That being said, the line has put together a few activities for when multiple families are onboard. There was a meet-and-greet pizza party on the first day and a video game night on another. Overall, however, families who bring younger children along should be prepared to entertain them on their own.