Aiming at coherence is a moral necessity. Serious people are serious about avoiding material inconsistency, as Aristotle noted in the Metaphysics, and Brandom has more recently thematized. (Unity of apperception is a moral imperative, not a fact, and certainly not something that could be simply possessed.) Reality or objectivity is measured by the counterfactual robustness of our generalizations; our ability to recognize incongruities; and our commitment to resolving them. Reality is not something you could point at, but a normative criterion, admitting of degree.
The thing that complements coherence is not correspondence, but rather non-correspondence. Putative correspondence provides no additional assurance of veracity, but non-correspondence tells us something is wrong with our conceptions, which is valuable information. From an intuition of incongruity arises a task to improve our understanding. (See also Error.)