All 7 Uses of

solemn
in
The Age of Innocence

Then the house had been boldly planned with a ball-room, so that, instead of squeezing through a narrow passage to get to it (as at the Chiverses') one marched solemnly down a vista of enfiladed drawing-rooms (the sea-green, the crimson and the bouton d'or), seeing from afar the many-candled lustres reflected in the polished parquetry, and beyond that the depths of a conservatory where camellias and tree-ferns arched their costly foliage over seats of black and gold bamboo.†
Chpt 3

solemnly = with seriousness and dignity

Their large solemn house in Madison Avenue was seldom opened, and when they came to town they received in it only their most intimate friends.†
Chpt 6 *

solemn = very serious--possibly dignified

The double doors had solemnly reopened and between them appeared Mr. Henry van der Luyden, tall, spare and frock-coated, with faded fair hair, a straight nose like his wife's and the same look of frozen gentleness in eyes that were merely pale grey instead of pale blue.†
Chpt 7

solemnly = with seriousness and dignity

The occasion was a solemn one, and he wondered a little nervously how she would carry it off.†
Chpt 8

solemn = very serious--possibly dignified

After the portieres had solemnly closed behind their visitor a silence fell upon the Archer family.†
Chpt 10

solemnly = with seriousness and dignity

Her large pink face was appropriately solemn, and her plum-coloured satin with pale blue side-panels, and blue ostrich plumes in a small satin bonnet, met with general approval; but before she had settled herself with a stately rustle in the pew opposite Mrs. Archer's the spectators were craning their necks to see who was coming after her.†
Chpt 19

solemn = very serious--possibly dignified

And he understood for the first time the earnestness with which May, who was incapable of tying a ribbon in her hair to charm him, had gone through the solemn rite of selecting and ordering her extensive wardrobe.†
Chpt 20

Definitions:

(1) (solemn)
in a very serious (and often dignified) manner
(2) (meaning too rare to warrant focus)
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.