The word "elegize" is a verb that means to compose an elegy, which is a poem or piece of writing that expresses sorrow or lament for someone who has died. When you elegize someone, you are honoring their memory and expressing your feelings of loss.
While primarily used in the context of death, "elegize" can also be used more broadly to express sorrow for something that has been lost, such as a tradition or a past era.
There aren’t specific idioms or phrasal verbs directly associated with "elegize," but you might find phrases like "pay tribute to" or "sing the praises of" to express similar sentiments of honoring someone.
In summary, "elegize" is about paying respect through words, especially in the form of poetry, for someone who has died or for something that is lost.