Optical interconnects have attracted significant research interest for use in short-reach board-level optical communication links in supercomputers and data centres. Multimode polymer waveguides in particular constitute an attractive technology for on-board optical interconnects as they provide high bandwidth, offer relaxed alignment tolerances, and can be cost-effectively integrated onto standard printed circuit boards (PCBs). However, the continuing improvements in bandwidth performance of optical sources make it important to investigate approaches to develop high bandwidth polymer waveguides. In this paper, we present dispersion studies on a graded-index (GI) waveguide in siloxane materials designed to deliver high bandwidth over a range of launch conditions. Bandwidth-length products of >70 GHzxm and ~65 GHzxm are observed using a 50/125 um multimode fibre (MMF) launch for input offsets of +/- 10 um without and with the use of a mode mixer respectively; and enhanced values of >100 GHzxm are found under a 10x microscope objective launch for input offsets of ~18 x 20 um^2. The large range of offsets is within the -1 dB alignment tolerances. A theoretical model is developed using the measured refractive index profile of the waveguide, and general agreement is found with experimental bandwidth measurements. The reported results clearly demonstrate the potential of this technology for use in high-speed board-level optical links, and indicate that data transmission of 100 Gb/s over a multimode polymer waveguide is feasible with appropriate refractive index engineering.