I’ve been working a lot with two single-board computers recently: the Raspberry Pi 3 and the ESP-8266. Both of these include (and that’s why they’re so attractive to me) WiFi hardware.
WiFi devices, because they’re broadcasting a radio signal, use a fair amount of power. Higher-power processors, such as those on the Raspberry Pi, also can consume a lot.
Cheap power supplies, such as most wall-warts, come in two varieties. Unregulated power supplies might produce two or three times the rated voltage when the load is drawing very little current, while they generally produce quite a bit less than the rated voltage when the load draws a lot of current. Regulated power supplies do a bit better – they generally don’t produce a lot more than their rated voltage. However, my recent testing indicates that they don’t generally hold their rated voltage at their maximum rated current.
The way to test a power supply (or a battery, or a radio transmitter) is to use an electronic load. These can be programmed to draw a fixed current, for example, regardless of the voltage. If it slowly (in steps) increases the current draw, and at each step measures the voltage provided by the power supply, one can look at the graph and see the performance of the power supply.
The following link provides a little more detail and some examples. It also links to a very good vlog by Andreas Speiss – he has a ton of interesting material on his YouTube channel.