Both Uses

solemn
in
The Remains of the Day
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A solemnness hung in the air after she said this, until eventually Mr Taylor said to me: "Harry here does a lot of organizing for our local member.†
Chpt 3e -

solemnness = seriousness
Indeed, the distinguished gentlemen continued to smoke their cigars, solemn expressions on their faces, not uttering a word, while his lordship instructed me to bring up a certain exceptionally fine bottle of port from the cellar.†
Chpt 4a - *

solemn = very serious--possibly dignified

Definitions:

(1) (solemn)
in a very serious (and often dignified) manner
(2) (meaning too rare to warrant focus)
Less commonly, solemn can mean that something was done with great or appropriate ceremony. It can also be used to describe something as dark or undecorated.