This month, Roy Rogers Jr. parted with Trigger, the horse made famous by his singing cowboy father.

Mr. Rogers and his siblings kept the palomino, mounted and preserved, in the family museum in Branson, Mo., before its doors closed last year. The horse sold for $266,500 at Christie’s in New York, one of 300-odd items, including cowboy boots, belt buckles and guitars, bequeathed to the Rogers family after their father’s death.

“I grew up with a lot of these things,” says Mr. Rogers, who goes by the nickname “Dusty.” “My dad told us years ago, when you get to the point where it costs a lot of money, when it becomes demanding to keep things, it’s OK to let them go. It’s been a very difficult decision.”

All told, some $41 trillion in wealth will transfer between generations over the next four decades, according to the Boston College Center on Wealth and Philanthropy. A significant portion will be in the form of art, jewelry and other heirlooms that have filled attics, safe-deposit boxes and hallways for decades—and for which economic values can be as difficult to ascertain as sentimental ones.

That can lead to major headaches when it comes to settling estates, especially this year. In most years, you simply need to determine the value of an heirloom on the owner’s date of death for tax purposes. But this year, with the estate tax temporarily suspended, things are far more complex. Very wealthy families will benefit as estates pass to the next generation tax-free. But those that are merely affluent may get hammered.

Ride ‘em, Christie’s: Roy Rogers’s stuffed horse, Trigger, sold for $266,500 at auction this month. Trigger and his taxidermied dog, Bullet. (Photo by Jemal Countess/Getty Images)