In high-power fibre-optic beam delivery systems using Nd: YAG lasers, it is vital that power is coupled into the fibre core with very high efficiency, in order to avoid damage to the fibre, its cable and the beam delivery optics. We have shown that by measuring the optical power propagating in the cladding of the fibre, it is possible to monitor the coupling efficiency with much greater sensitivity than is available when the core-guided power is measured. We have developed a theory describing the power in the cladding of the fibre as a function of the launching conditions for a number of types of beam misalignment, and hence as a function of coupling efficiency. We have constructed and evaluated an optical device for monitoring cladding power, and conducted experiments which have validated our theoretical model. We have noted the implications of the cladding power monitoring device in the measurement of coupling efficiency, and have indicated other potential applications for fibre-optic beam delivery systems.