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[Tor]

The point about 'amperage' is that it, unlike 'voltage', isn't something to be concerned about. Voltage is critical though.

e.g. A charging port can be labelled '5V', which means that the charger must provide 5V, and not 4V or 6V. This is critical, so you mark the port with the voltage (so that you won't connect a charger with the wrong voltage). However, it doesn't matter if the charger provides 500mA or 1A or 2A or 10A. That's not important at all. It only means it will charge slower if under some level, and faster if the charger can provide more (up to a point, for this device probably somewhere between 1 and 2 amps).

Some folks think that a charger marked '5V, 2A', will "push" 2A, so that a charger with "too high" ampere rating can damage the device. This is not the case.

You will want to mark chargers with the amperage, but for battery-powered devices there's not usually much need to specify that. Unlike non-battery powered devices, where you don't charge. If, say, an amplifier needs a 2A current at 12 volts to operate, it'll be labelled as such. Then you can go look for a 12-volt PSU which can provide 2A or more.

 

[mali]

If the PSU isn't able to provide enough current it might overheat. So you should have a PSU rated at the correct current or above, not the other way around.

Edit:
It depends on the "smartness" of the PSU, though. Good quality chargers will provide what they can without overheating.

 

[Tor]

Go bigger rather than smaller. The only problem with a big on (as in, say, 50A) is that if you short-circuit it there'll be a bigger bang...