Spinon confinement is key to the understanding of quantized excitation spectra in quasi-one-dimensional
S = \textonehalf{} spin systems. The authors investigate the quantization of the excitation continuum in quasi-one-dimensional
S=1 antiferromagnetic spin systems with single-ion anisotropy
D. When
D 0, the magnon continuum is quantized by the interchain interactions. This is due to magnon confinement. The present study suggests the possibility for observation of quantized spectra in many
S=1 antiferromagnetic spin-chain compounds.