The problem is that many eBay/Chinese suppliers play the same game as amplifier makers used to so that a nominal (say) 1000 watt inverter actually says in the description that it can't supply 1000 watts continuously. Reading the very few reviews one can find shows that in many cases the reality is that inverters can't supply anywhere near their rated output.
However, on the other hand, there are excellent inverters available at very reasonable prices. The inverter I currently have is a nominal 500 watt one that cost me £25 back in 2012 and it copes admirably with just about everything I throw at it plus giving up gracefully when I ask too much. Among other things it runs an ordinary domestic refrigerator without problems and fridges are supposedly one of the more difficult loads for inverters.
The 500 watt inverter is a 'modified sine wave' one, I want a the larger, sine wave one to run a microwave among other things.
So how do I find a supplier as good as the one who made my old 500 watt inverter? I can't take a look at it just now but I suppose that might be one approach, get another from the same manufacturer if they make 'pure sine' inverters. However any other recommendations of good suppliers or other ways to find good manufacturers would be most welcome.