Frequency and width crossing have been observed for two coupled resonances
in a microwave cavity. The cavity consisted of two nearly identical rectang
ular boxes. The boxes were coupled by a slit of variable width. The data ar
e well described by a non-Hermitean S matrix leading to a 2x2 non-Hermitean
effective Hamiltonian. The values of the interaction strength \v\ for whic
h width crossing and frequency crossing, respectively, were observed, are a
bove and below a critical value \v(c)\ for which one expects a joint freque
ncy and width crossing.