In some versions of Civ, you can switch production to a different wonder or building, sometimes at a penalty. Civ V no longer has production switching (a good design decision in my book) and so just gives you a "cash refund", converting the wasted production into money. Still, this is pretty frustrating - the money may be quite useless to you.
Civ V also introduced National Wonders, of which each civilisation can build one - the National Epic, Circus Maximus, etc. My idea is that each World Wonder should have a National Wonder counterpart to which production automatically switches if you lose the race.
This makes sense from a flavour point of view: if you fail to build the Notre Dame - that is, the really famous cathedral, you'd still end up building a somewhat famous cathedral. Or your pyramids may not be as grand and famous and ancient as the ones next door, but they're still pretty impressive.
To preserve the uniqueness of World Wonders, these lesser variants would have more humdrum versions of their counterparts' effects. Where this isn't possible, the difference could be that building the World Wonder version, the famous one, produces a big one-time burst of culture.
This isn't really a fully fleshed-out idea, and it might make Wonders less exciting, but it would reduce the weird spooky-action-at-a-distance thing where a Civ you haven't even met building a wonder somehow stops you from building yours!