Both Uses

nevertheless
in
A Man for All Seasons
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Nevertheless, and though you have heinously offended the King's Majesty, we hope if you will even now forthink and repent of your obstinate opinions, you may still taste his gracious pardon.†
Chpt 2 *

nevertheless = despite that (used to connect contrasting ideas)
Would God my death might do him some good ....(With a great flash of scorn and anger) Nevertheless, it is not for the Supremacy that you have sought my blood-but because I would not bend to the marriage!†
Chpt 2

Definitions:

(1) (nevertheless)
despite that

Based on idea 1 we might not expect idea 2, but this is a way of saying that even though idea 1 was just stated, we still have idea 2. Synonyms include in spite of that, despite that, nevertheless, nonetheless, on the other hand, in contrast and but.
(2) (meaning too rare to warrant focus)