I noticed that 仰ぐ and 見上げる both mean "to look up." What difference do these two have in terms of nuance and usage? I'd appreciate it if there would be sample sentences taken from corpus.
見上げる is a simple compound verb that means looking up at something that is located above you.
仰ぐ is sometimes used in this sense, too, in which case it sounds more literary and/or poetic. 天を仰ぐ means looking up at the sky after being shocked, grieved, etc. It's always used transitively; without を, あおぐ alone makes little sense. Basically this is not used in everyday conversations outside of a few fixed idioms.
Note that 仰ぐ today mainly means "to see someone (a teacher, senior, etc) as a respectable person" (e.g, 彼を師匠と仰ぐ) and "to seek/take direction (from a boss, etc)" (e.g., 上司の指示を仰ぐ).