This conjunction is completely intransparent, in other words we can't deduce the meaning from its componentes. The no is a relict of ancient times, because no doesn't exist in modern Portuguese. Entanto is equivalent to entretanto, meanwhile. One could be induced to assume that no has something to do with the negation particle no that we have in Spanish and Italian., however this is not the case. Translated literally we would get not meanwhile or something like that, what has nothing to do with the actual meaning. (What explains why the no didn't developped to não. In the consciousness of the speakers it has nothing to do with the negation particle não. The conjunction no entanto suggests therefore something that has nothing to do with the actual meaning.
no entanto despiete of
Eu vejo tudo, no entanto não vejo nada.*
I see everything, but I see nothing.
Levei um guarda-chuva, no entanto não precisei usá-lo.
I took an umbrella with me, but I didn't use it.
Eles não são, no entanto, os mesmos.
However they are not the same.
Não fazemos aquilo que queremos e, no entanto, somos responsáveis por aquilo que somos.
We don't do what we want, however we are responsible for what we are.
* That happens. The world must be interpreted. To see it is only the beginning of unserstanding.