All 3 Uses of

solemn

in

Hamlet, Prince of Denmark

'Tis not alone my inky cloak, good mother, Nor customary suits of solemn black, Nor windy suspiration of forc'd breath, No, nor the fruitful river in the eye, Nor the dejected 'havior of the visage, Together with all forms, moods, shows of grief, That can denote me truly: these, indeed, seem; For they are actions that a man might play; But I have that within which passeth show; These but the trappings and the suits of woe.†
Scene 1.2

solemn = very serious--possibly dignified

A figure like your father, Armed at point exactly, cap-a-pe, Appears before them and with solemn march Goes slow and stately by them: thrice he walk'd By their oppress'd and fear-surprised eyes, Within his truncheon's length; whilst they, distill'd Almost to jelly with the act of fear, Stand dumb, and speak not to him.†
Scene 1.2 *

let me see:— We'll make a solemn wager on your cunnings,— I ha't: When in your motion you are hot and dry,— As make your bouts more violent to that end,— And that he calls for drink, I'll have prepar'd him A chalice for the nonce; whereon but sipping, If he by chance escape your venom'd stuck, Our purpose may hold there.†
Scene 4.7

Definition:

in a very serious (and often dignified) manner