I had always believed until now the right term was prevaricate ('to speak or act in an evasive way').
But the (multiword) phrase "she ummed and ahhed""ummed and ahhed" is accepted.
I don't think the answers referencing dysfluencies and speech pathologies are relevant since that's not the typical reason. It's usually because the speaker is embarrassed, flustered or caught doing something they can't explain.