Emil was afraid during much of his time following Grundeis through the streets and cafes of Berlin.
He was afraid of losing the thief in the crowd and afraid of being noticed and afraid of running out of options.
These fears were rational — he was one small boy in a large unfamiliar city pursuing a grown man who had already robbed him once.
But Emil had decided that the fear was not a sufficient reason to stop, and so he experienced the fear and kept going anyway.
The other children felt fear too — some of them worried that the thief might become violent or that the police would not believe them.
But they had each made the same decision Emil had made: the fear was real and the action was still required regardless of the feeling.
Kästner presents this as the working definition of bravery that his young characters demonstrate again and again throughout the story.
Bravery means acting despite fear.

The concept of bravery that Emil and the Detectives proposes is philosophically precise in a way that rewards attention.
The novel consistently distinguishes between fearlessness — which Emil clearly does not possess — and bravery, which he clearly does.
Fearlessness would mean that Emil follows the thief without experiencing anything recognizable as fear along the way.
Bravery means that Emil experiences the fear fully and chooses to continue acting in spite of it because the action is required.
This distinction matters because it locates the moral credit correctly — in the choice to act rather than in the absence of feeling.
A person who does something difficult without fear deserves no particular credit — they simply lacked the normal response.
A person who does something difficult while experiencing fear has made a genuine and costly moral decision and deserves real credit.
Kästner's children are brave in this precise and meaningful sense, which is why their eventual success feels genuinely earned.
Bravery means acting despite fear.