We report on measurements of delay time corresponding to evanescent coupled-cavity modes in three-dimensional photonic crystals. By creating a defect inside the crystal, photons are confined within a boxlike cavity of volume ∼(λ/2)3. It is observed that photon lifetime increases drastically and group velocity of photons tends towards zero at the waveguiding band edges of the periodic coupled cavities. Experimental results are well explained within the classical wave analog of the tight-binding picture. Observation of the extremely small group velocity and long photon lifetime at the coupled-cavity waveguide band edges have important potential applications.