Atari ST and Amiga computers used a frequency that many modern VGA monitors cannot deal with - 15kHz horizontal frequency. Even when you physically adapt the monitor the fit the computer plug you will usually see no picture or a "Sync out of Range" message. There are some CRTs and even newer LCDs that can accept the 15kHz signal however, once you build an Atari/Amiga to VGA cable or adapter.

There are some lists of monitors known to work - for instance:

15khz.net

15khz.wikidot.com

However, many monitors are not listed. Therefore there is a great GitHub project that programs an Arduino to output 15kHz VGA so you can tell if your monitor accepts the signal. There are even some carrier boards for the Arduino:

http://www.gammon.com.au/forum/?id=11608

https://github.com/planeturban/15khzvgatester

I had Arduino Nanos lying around that I wanted to use - so I made this carrier which I can power from a USB power bank, 9v battery, or a barrel jack.

Use the color software from the 15khzvgatester to upload to your Arduino.

You can find the female DB-15HD jack yourself or even solder on to half of a VGA cable.

A successful test is seeing the pattern of colored boxes as above - the monitor is likely to display from an Atari ST or Amiga.

Sync out of range errors, half the screen filling, no picture, etc are very unlikely to work.