Formal. Something ignominious makes you lose face in front of other people. The key idea is public shame, not private guilt. That is why it lives with a small set of nouns you will see again and again: an ignominious defeat, an ignominious end, an ignominious exit, an ignominious retreat. Sports writing and political writing love it — a team knocked out in the first round, a minister who has to resign over a scandal. There is a useful difference between this word and 'ignoble': ignoble is about the quality of your motives (low, unworthy); ignominious is about how it looks when it goes wrong in public. You can lose ignominiously without doing anything morally wrong at all — you just lost badly, and everyone saw. Because it is long and formal, it also gets used half-jokingly for small embarrassments: 'my ignominious failure to open the jar'. That joking use is common and worth knowing.