  The Hong-Ou-Mandel effect is considered a signature of the quantumness of
light, as the dip in coincidence probability using semi-classical theories has
an upper bound of 50%. Here we show, theoretically and experimentally, that,
with proper phase control of the signals, classical pulses can mimic a
Hong-Ou-Mandel-like dip. We demonstrate a dip of 99.635 +/- 0.002% with
classical microwave fields. Quantumness manifests in wave-particle
complementarity of the two-photon state. We construct quantum and classical
interferometers for the complementarity test and show that while the two-photon
state shows wave-particle complementarity, the classical pulses do not.
