Basis risk is an important consideration when hedging longevity risk with instruments based on longevity indices, since the longevity experience of the hedged exposure may differ from that of the index. As a result, any decision to execute an index-based hedge requires a framework for (i) developing an informed understanding of the basis risk, (ii) appropriately calibrating the hedging instrument and (iii) evaluating hedge effectiveness. We describe such a framework and apply it to two case studies: one for the UK (which compares the population of assured lives from the Continuous Mortality Investigation with the England & Wales national population) and one for the US (which compares the population of California with the US national population). The framework is founded on an analysis of historical experience data, together with an appreciation of the contextual relationship between the two related populations in social, economic and demographic terms. Despite the different demographic profiles, each case study provides evidence of stable long-term relationships between the mortality experiences of the two populations. This suggests the important result that high levels of hedge effectiveness should be achievable with appropriately-calibrated, static, index-based longevity hedges. Indeed, this is borne out in detailed calculations of hedge effectiveness for hypothetical pension portfolios where the basis risk is based on these case studies.