Example : A grave God-fearing man.
A quiet sedate nature.
As sober as a judge.
A solemn promise.
The judge was solemn as he pronounced sentence.

Synonyms : grave, sedate, sober

Example : Both sides were deeply in earnest, even passionate.
An entirely sincere and cruel tyrant.
A film with a solemn social message.

Synonyms : earnest, sincere