A "solemn procession" is a formal and serious parade or march, where people walk together in a respectful and reverent manner, often during religious or ceremonial events. Full definition
On a day rich with symbolism, the scarlet - clad cardinals entered the Sistine Chapel in solemn procession, chanting prayers and watched over by the paintings of Renaissance artist Michelangelo. (religion.blogs.cnn.com)
It deserves every dissent from the Met's solemn procession of aging modern British painters. (haberarts.com)
With their long metal canes striking loudly on the stone pavement, the guards announced the solemn procession and cleared a path through the narrow streets crowded with worshipers. (religion-online.org)