It is known that quantum fluctuations significantly modify the energy required to produce a mobile domain wall, or soliton, on a chain of exchange-coupled magnetic atoms subject to an anisotropy field or magnetic field. The authors show here that spin-wave theory applied about the classical soliton to the sine-Gordon equation can be adapted to calculate these zero-point energy effects by matrix diagonalisation. The results for solitons on ferromagnetically coupled chains are qualitatively similar to those obtained by other techniques. In antiferromagnets, however, the quantum fluctuations appear to produce, under certain conditions, a negative soliton creation energy, i.e. a soliton-containing ground state. This situation is a result of the non-linear response of the zero-point energy to small changes in the effective anisotropy of the one-dimensional antiferromagnet.