How exactly can she be given a judgment when she cannot speak? The most crucial part of a judgment is the commentary and self reflection that a hero has about the entire experience and what is happening.

Sona clearly cannot communicate beyond her music so....?

Internal thought and emotions are often conveyed by music. The Judgement can manipulate the mind and cause thoughts in their patient's minds. I'm sure that the team has something very awesome planned for her League Judgement.

You'd be surprised how expressive music can be, a lot of emotions and feelings can be expressed purely through sound.

Mental communication. One who does not speak will probably have a lot running through their mind.

Sign language?

Most of the judgements thus far have mostly been composed of what the champion is thinking, feeling and telling us their gestures indicating their current mood and take on the situation. I find the dialogue in the judgments to be minimal and thus it will not be too hard for us to understand what Sona would be trying to convey.

I thought one of the key aspects of the judgement was the "opening of the mind".

The summoners are linked to champions through their mind, and can see and feel all the champions see or feel.

Dialogue is not necessary for the judgement.