This is a question that I have been asked many times over the years and the simple answer is that they are. Children pose no risks to using noise cancelling headphones as along as they keep the volume below (how many decibels).
Noise-canceling headphones have been designed to reduce background noise by producing an “anti-noise” sound wave that interferes with any background noise. The design of the headphones includes a microphone and electric circuitry that generates the opposing sound and unlike smartphones, does not emit low level radiation.
This type of headphones have been designed to help the user listen to music without the interference of background noise that disturbs their music. For children, we can use this technology to help reduce noise and help promote sleep where there is background noise. An example of this would be on an airplane where the sound of the engines tends to interfere with children trying to sleep.
By using a noise cancelling headphone, firstly children will not have turn the volume up so high and therefore not risk damaging their sensitive ears, but we can also use the technology to create a quieter environment for children which in turn will help to promote sleeping, especially in noisy situations.