I believe they're like tamen and vērō, except with nec before...
They might be translated a whole variety of ways depending on context, but the basic meanings are nec vērō = but not, and nec tamen = however not/and yet not. For instance, taking examples from the textbook I use, with my literal translations:
Homō sex diēs cibō carēre potest, nec tamen fame moritur = Man can be deprived of food for six days,
and yet not die from hunger. (even more literally: "and yet he doesn't die from hunger")
Neque tamen classis Rōmāna omnēs nautās quī ubīque nāvigant tuēri potest =
However, the Roman fleet can
not protect all the sailors who navigate everywhere.
Mēdus surgere cōnātur, nec vērō sē locō movēre potest = Medus tries to get up,
but he can
not move (from there).
Nōs quoque saepe interrogāmur, nec vērō prāvē respondēmus = We too are often interrogated,
but we do
not answer wrongly.