Performance analysis of embedded firmware
Yes, it's called an ammeter.  It measures current.  Any common "multimeter" will have ammeter capability.  For the test, run the unit from a fixed voltage supply and put the ammeter in series.  Since voltage is fixed, current is proportional to power.  You can then experiment with different software options to see what draws what current.

However, while I've worked on a number of power-sensitive microcontroller designs, I don't recall measuring current during the design phase.  At most this was done as part of verification to make sure the current was within the range that I already knew it would be.

Actually measuring current only tells you what that unit at that temperature with that voltage is doing right now.  It doesn't tell you what the worst case could be, which is usually what you need to design for.

Designing a system for low power shouldn't be a trial and error procedure.  You look at the datasheets carefully to see what draws what power under what conditions, then sit down and actually design the system deliberately to exploit those characteristics to minimize power.  Measurements should only be to verify that you didn't screw up or that something unexpected isn't happening.

When designing for low power, make sure to consider the whole system, not just the load.  Minimizing power usage of the load is important, but how the power supply delivers that power can also be important.