Among luxury connoisseurs, the name Cartier is likely to conjure images of sumptuous jewels and classic 20th-century wristwatch designs, à la the iconic Santos and Tank models. But until recently, aficionados of fine watchmaking had to look elsewhere to find timepieces worthy of their interest.

That changed in 2008 when Cartier debuted its Fine Watchmaking Collection. The designs aimed for the horological stars with complicated wonders of timekeeping, such as the Rotonde de Cartier Astroregulateur …