  We derive analytical formulas quantifying radiative emission from
subwavelength emitters embedded in triply resonant nonlinear $\chi^{(2)}$
cavities supporting exceptional points (EP) made of dark and leaky modes. We
show that the up-converted radiation rate in such a system can be greatly
enhanced---by up to two orders of magnitude---compared to typical Purcell
factors achievable in non-degenerate cavities, for both monochromatic and
broadband emitters. We provide a proof-of-concept demonstration by studying an
inverse-designed 2D photonic-crystal slab that supports an EP formed out of a
Dirac cone at the emission frequency and a phase-matched, leaky-mode resonance
at the second harmonic frequency.
