Estimating the engagement of children is an essential prerequisite for constructing natural Child-Robot Interaction. Especially in the case of children with Autism Spectrum Disorder, monitoring the engagement of the other party allows robots to adjust their actions according to the educational and therapeutic goals in hand. In this work we delve into engagement estimation with a focus on children with autism spectrum disorder. We propose deep convolutional architectures for engagement estimation that outperform previous methods, and explore their performance under variable conditions, in four databases depicting ASD and TD children interacting with robots or humans.