Fourteen Caribbean nations and a British law firm are trying to find the solution to a puzzle that has eluded many economists, historians and activists: how to put a price tag on the harm wrought by slavery, and then persuade someone to pay.

Members of the Caribbean Community, a regional bloc, have hired London firm Leigh Day to help them prepare a suit for the International Court of Justice. The countries plan to seek reparations from the U.K., France and the Netherlands for the lasting effects of the slave trade, which over four centuries brought millions of people against their will from Africa to European colonies in the Caribbean region.

The legal challenges to seeking reparations are immense: Countries must prove crimes committed by—and against—long-dead people.

But the bigger difficulty may be setting a price tag. Scholars have sought to quantify reparations for as long as activists have sought them—for slavery and, in the U.S., for racial discrimination after the Civil War. There are many approaches, from calculating lost wages over the years to tallying disparities in health that can be tied to slavery. All produce widely varying figures, and the sheer size of many of the numbers has been an impediment to the reparations movement.

Martyn Day, founding partner of Leigh Day, said his clients are working to document the legacy of slavery for today's Caribbean residents, such as the economic effects of being unable to accumulate wealth over the centuries, and elevated diabetes rates due to the diet imposed on slaves and passed down the generations. "What in the end will all that work out to?" Mr. Day said. "I have no idea."