There are many tie-ins between the two: both are “doers,” there are similarities in how they made their case within and beyond their field, and both worked on externalities — with Nordhaus most famous for his work on negative environmental externalities and Romer most famous for his description of positive externalities in the form of ideas. (Nordhaus, it must be noted, has done seminal work on positive externalities, too.)
To me, though, the most obvious connection between them is with an eye toward the future: among the biggest challenges society faces is encouraging innovation and economic growth without destroying the environment, most notably through climate change. Romer and Nordhaus have done more than almost anyone to address that challenge.
In honor of their work, here are a few things related to it:
As for Romer, here’s his plain English overview of economic growth. Here’s a video by Marginal Revolution University on his work. And the excellent book Knowledge and the Wealth of Nations, by David Warsh, tracks Romer’s essential contribution to economics, with lots of great historical context.