How can I test the maximum current an outlet will provide?
It's called a Kill-A-Watt

A testing instrument that tells you what your appliances are currently drawing.  



But you don't load up the circuit to breaker trip, because that would be reckless and unsafe.  You use it (or them) measure the actual current draw of the other loads and add them up.  

You must also multiply any continuous loads by 125% when factoring. 

Example: You have a 20A circuit. 


1 amp of floor lamp
5 amps (a 4 amp PC, on continuously so rated 125%) 
8 amps of air conditioner


That leaves 6 amps usable for a non-continuous load, or 4.8A for a continuous load.