Quantum conductance of narrow constrictions between two wide two-dimensional regions is obtained by using the recursive transfer-matrix technique to evaluate the Kubo formula exactly. Consistent with recent experimental findings, the conductance is found to be quantized in steps of 2${e}^{2}$/h only under a restricted set of optimal conditions. Detailed numerical results are given as functions of temperature, elastic and inelastic scattering strengths, and constriction geometry. The quantization disappears at very low temperatures due to quantum resonances and for strong elastic scattering due to conductance fluctuation effects. The law of series addition of resistances is found to be invalid for these quantum constrictions.