What is the highest air pressure a barometer can measure?

It depends, a barometer can measure many different types of air pressure and there are different kinds of air pressure. your best bet would be to identify what type of barometer you have and simply read a dial. If you don't have a barometer and would just like to know what the maximum registered amount for high pressure is then you should consult you weather records centre. These following records i believe are the most up to date: 1085.6 mb in Mongolia. The lowest recorded air pressure is 850 mbar in Manchester, South Dakota. In theory a barometer can record any amount of air pressure depending on its size. The larger the barometer, the greater range of measurement of air pressure. Currently the worlds largest Barometer resides in the Denmark Visitor Centre. You can find more about this Barometer at: http://www.bertbolle.com/