I'm doing the assembly for these badges by hand so every component that I don't use is a time speedup. Looking at the blue LEDs for the badge, I decided to drive them without resistors. They have a forward voltage of 2.85V and at the high end I expect the coin cell to have 3.2V. Subtract the forward voltage and target 5 mA and here's our Ohms law:
You can expect a CR2032 to have an Internal resistance (IR or sometimes called ESR) to have 10-15 Ohms of resistance. That's a bit low, allowing between 23 mA and 35 mA to flow when the max continuous current for this LED is 15 mA.
Also, I don't want to have to do development with a battery. If I run this from a bench supply, I don't get the ESR benefit of the battery. I considered putting a footprint on the back for resistors, with a trace shorting them that could be cut for the development board. But in the end I opted to add a resistor network.
What resistance is best here? Ideally this LED should have 30 Ohms, assuming an (also ideal) 2.85V drop on a 3V supply and 5mA of drive:
I'm banking on 15 Ohms from the battery and using 15 Ohms on the board. This will drive the LEDs too hot during development but I'm taking my chances on that.