When more than one person (together) are travelling by air and more than one bag is being checked in, make certain you have the bags allocated to different passengers. The reason for this (as I have discovered) is that if/when more than one bag is delayed then you should also make certain more than one "file" is created (not necessarily possible if all bags are checked in onto one passenger's name - joined and shared allowance). If it is only one file then only one tranche of compensation may be offered even if more than one bag is delayed. Different airlines will have different rules and approaches, but had we taken the precaution I described (we were travelling together but on separate bookings and both bags were allocated to me, neither to her - oversight or through instruction ?), then for both my suitcase and hers delayed by days I would have got double the compensation I actually got. On check-in we will now insist on "naming" each bag separately and creating a separate file for each bag that goes missing - it cannot do us harm even if/when no compensation is on offer.
Nothing to do with compensation Karl, but what I do when travelling with someone else is put one change of my clothes in their case and vice versa so that if one case goes missing you've still got one change of clean clothes.