Insurance can, as has clearly been indicated in the literature, play an important role in dealing with catastrophe risks, not only as a compensation mechanism but also as a mechanism to influence the behaviour of the insured. It is the concept known as ‘insurance as governance’. However, we argue that there are limited possibilities for this role as far as the insurance of pandemics is concerned. The traditional technical tools, such as risk-based pricing, are difficult to apply. In addition, there may, ab initio, be serious problems in insuring pandemics within one of the main conditions of insurability (controlling moral hazard through an effective risk differentiation). One remedy that is traditionally applied, more particularly for natural catastrophes, is mandatory coverage. Furthermore, the capacity problem might potentially be solved through a multilayered approach in which, in addition to insurance and reinsurance, the government could also take up a role as reinsurer of last resort. That would also have the major advantage of stimulating market solution (and potentially providing incentives for the mitigation of damages), which clearly fails in a model where the government simply bails out operators. Finally, one important regulatory intervention is that insurers should be better informed than was apparently the case during the last pandemic about exactly which type of risks are covered and which are not.