  We examine how to signify and quantify the mesoscopic quantum coherence of
approximate two-mode NOON states and spin-squeezed two-mode Bose-Einstein
condensates (BEC). We identify two criteria that verify a nonzero quantum
coherence between states with quantum number different by $n$. These criteria
negate certain mixtures of quantum states, thereby signifying a generalised
$n$-scopic Schrodinger cat-type paradox. The first criterion is the correlation
$\langle\hat{a}^{\dagger n}\hat{b}^{n}\rangle\neq0$ (here $\hat{a}$ and
$\hat{b}$ are the boson operators for each mode). The correlation manifests as
interference fringes in $n$-particle detection probabilities and is also
measurable via quadrature phase amplitude and spin squeezing measurements.
Measurement of $\langle\hat{a}^{\dagger n}\hat{b}^{n}\rangle$ enables a
quantification of the overall $n$-th order quantum coherence, thus providing an
avenue for high efficiency verification of a high-fidelity photonic NOON
states. The second criterion is based on a quantification of the measurable
spin-squeezing parameter $\xi_{N}$. We apply the criteria to theoretical models
of NOON states in lossy interferometers and double-well trapped BECs. By
analysing existing BEC experiments, we demonstrate generalised atomic "kitten"
states and atomic quantum coherence with $n\gtrapprox10$ atoms.
