Verbal cognitive ability is known to correlate with emotion processing in faces and music in typically developing individuals. However, the relation between these variables among autistic people is not clear and has been investigated mainly in those who have proficient verbal cognitive ability. For this reason, we compared the recognition and perceived intensity of emotions in faces and music of 25 adolescents (12–16 years old) on the autism spectrum with lower (n = 12) or higher (n = 13) verbal cognitive ability. Participants were assessed with the verbal index of a cognitive test (WISC-V), an online hearing test, and two computer tasks that assessed emotion recognition using 4-second face and music stimuli. Participants were asked: (1) to identify the emotion conveyed in facial expressions and musical excerpts; and (2) to rate the intensity of that emotion. Participants were very accurate at identifying emotions (happiness, sadness, fear) in faces and music, irrespective of verbal cognitive ability. In fact, accuracy scores were near ceiling, which precluded a statistical comparison of emotion identification in faces and music. We discuss factors that likely influenced these results such as the level of task difficulty and the participants’ ages. In terms of intensity ratings in faces, sadness was perceived as less intense than happiness and fear. In music, intensity ratings of happiness, sadness and fear were similar within and between the groups with low or high verbal cognitive ability. Verbal cognitive ability was negatively associated with perceived emotional intensity in faces but not in music, which may indicate that language ability modulates the experience of facial emotional processing. On the basis of these findings, we suggest that adolescents across the autism spectrum might benefit from music education as a strength-based approach for teaching emotion processing skills.