WordNet sense 1 (dignified and somber in manner or character and committed to keeping promises):

sober, solemn, grave

WordNet sense 2 (concerned with work or important matters rather than play or trivialities):

serious

WordNet sense 3 (characterized by dignity and propriety):

staid

WordNet sense 4 (characterized by propriety and dignity and good taste in manners and conduct):

decorous

WordNet sense 5 (cause to be calm or quiet as by administering a sedative to):

calm, tranquilize, tranquillize, tranquillise