Right, CK and the others are right. There is, unfortunately, no accurate way of testing your camera meter without a second meter to check it against or sophisticated calibrating equipment.
The best way to test has already been suggested, that is, since you have two cameras, to compare the reading from each of them. To keep things constant, measure off the same, uniform surface. For example, a plain coloured wall or an opaque sheet of paper. Fill the frame, and take a reading, the two should match. If they don't then one is out... you will need to send one in for calibration.
A compromise if you only have one camera is to shoot a roll of slides with the camera's suggested meterings. In the frames where the camera shouldn't have got fooled, if the exposure if notably off then you may have a problem. Of course, this is inaccurate and will only show up gross problems with your meter.
Hope that helps.
PS= not sure what you're describing abt the Zone system, doesn't ring any bells for me.