Interferometers form a cornerstone of precision measurement, leveraging wave superposition and phase coherence to convert minute physical perturbations into measurable intensity variations. Here, we establish how paradigmatic interferometric architectures, the canonical Michelson and Mach-Zehnder interferometers, can be endowed with entirely new operating principles by replacing conventional beam splitters with judiciously designed non-Hermitian resonators. To uncover how non-Hermitian physics can assist in interferometry, we subject these canonical interferometers to a modern non-Hermitian symmetry analysis. A fundamentally transformed interference landscape then arises when the resonators and interference pathways collectively induce partially deficient spectral degeneracies, mathematically characterized as multimode versions of exceptional points. Key characteristics of these exceptional interferometers are nonanalytic destructive interference conditions, resulting in distinct bright-fringe and dark-fringe operating regimes organized by non-Hermitian winding and braiding topology. By revealing how exceptional-point-assisted interference reshapes the canonical geometries, our findings transfer central paradigms of non-Hermitian spectroscopy into the interferometric setting, and establish exceptional-point interferometry as a new platform-independent paradigm for general-purpose precision sensing, applicable from on-chip photonics to macroscopic observatories.