'solemn man' is a correct and usable phrase in written English.
You can use it to describe a man who may appear serious or even sad in demeanor. For example, "The man standing in the corner with his arms crossed looked like a solemn man."
Author of "An American Tragedy" is solemn man.
And then a solemn man in a dark suit appeared, and we were invited in to peruse the catalogue.
He is a gentle, solemn man, and this is as heated as I will see him get.
Dave Chasen, a small, solemn man with soft, wistful eyes, came over and told Schary how happy he was to see him there.
A solemn man with tremendous self-discipline and unfaltering faith in himself, Treasury Secretary Chase faced the greatest challenge of his career — and the most urgent of the many problems plaguing the Union in those tense months after Fort Sumter.
My guide, a solemn man named C.K. Gupta, is deeply apologetic.
San Fermin's collective ardor reinvigorates familiar indie tropes: the analog eclecticism, the lavish harmonies, the songbird women, and the solemn men.
And its taste for pompous honorifics and ornate regalia may conjure images of solemn men with arms interlocked: Laurel and Hardy meet Babbitt.
And what makes the image of these bereaved and solemn men so moving is not just their intimacy in grief but that Titianesque counterplay: the arrangement of heads against dazzling daylight.
This juxtaposition was perhaps illustrative of the awful confusion of our era--in the one chamber the determined ladies conferring about an activity that not so long ago was an exclusively male pastime, in the adjoining chamber solemn men discussing an intimate feminine topic.
Waiting at Biggin Hill airport on Friday was a solemn white man holding a square placard.
