Two quick-and-dirty Arduino Power Current Taps for the Arduino Survival Guide: Workbench Edition class I taught for SqWr a while ago. These give you the current drawn by the entire board + LEDs + whatever, so you can calculate the power dissipation in that poor on-board regulator.
The USB version:
The general idea is to cut a USB extension cable (Type A plug on one end, Type A receptacle on the other) in half, splice the two data wires, splice the ground / common wire, but connect the +5 V wires to a dual banana plug that goes into a current meter. The Big Box o’ USB Junk produced a cutoff cable end with a Type A plug and a PC jumper that was supposed to connect an internal USB header to the back panel; the red blob of silicone tape conceals the jumper’s socket strip and a five-pin male header with all the wires soldered to it.
You could use a Type B plug that would go directly into an Arduino UNO (or similar), but I figured this way everybody can bring whatever cable they need for their particular Arduino, not all of which have bulky Type B receptacles these days.
The External Power version:
The coaxial power plug goes into the Arduino and whatever you used for power goes into the socket. The Big Box o’ Coaxial Power Stuff actually had a more-or-less properly sized coaxial jack with two wires on it and silicone tape wrapped around it; I regarded that as a Good Omen and pressed it into service as-is.
These will also replace the horribly rickety collection of alligator clip leads I usually use for such measurements…