Is there any standard formula for matching for the two? Obviously, you need a wider tire on a wider rim, and vice versa.

The reason I ask is I've just bought my first new bike in about twenty two years (a Surly Karate Monkey frame) and am trying to figure out what rims to stick on it... I'm tenatively planning to run 700x32's on it, which should be about equivalent in width to the 1.25 slicks I used to run on my commuter, which is what this bike is replacing.

Thanks in advance.

Nice frame!. I would strongly consider building a wheelset using 700c touring rims which are slightly wider than your standard racing road rims. You can easily mount 40mm tires on these rims. Your new frame has certainly plenty of room for even wider rubber. Are you building it as standard geared commuter or a single-speeder?

Sheldon brown has a graph showing rim width vs tire width should give you a idea what width rim you will need.
https://www.sheldonbrown.com/tire_sizing.html

Should've known to check Sheldon Brown, thanks!

The bike will have a seven speed (freehub) rear hub with nexus roller brake. I'm as yet undecided as to if I'll have one, two, or three rings on the crank.

Consider Mavic MA-3s.

I run x35s and x32s on my commuter with Mavic MA-2s, which were replaced by the MA-3s. I've heard Mavic doesn't necessarily condone this combination, but I've been using it for years after reading a recommendation by Jobst Brandt in rec.bicycles. I've used Conti Top Touring (x35s and x32s, wire bead) and, currently, Avocet Cross IIs (x35s, kevlar bead). The Cross II x35 has a cross section size similar to the TT x32.

Generally, you run maybe 90psi max in x32s... hardly enough to be a problem with a good, solid rim.

Yes.....MA-3's (currently available) are tough rims. I even had Specialized Nimbus 41's on them a while back.....not a problem....