How do digital mulitimeters (DMM) measure capacitance through their typical 10M Ohm input/output impedance?
Providing a logic level of 3.3V, attempting to measure 1F would mean a time constant of 10M seconds (R x C) thus the voltage rise in the capacitor being in immeasurable (in the noise floor.) They also do it within a second or so at 3% accuracy. How on earth is this achieved?
There are many ways to measure capacitance, If you have a waveform generator you can either use a square wave and measure the rise time. Or a sine wave and measure the current and voltage. If you know current and voltage, you know what your load is. If the load is a capacitor, you'd also need phase information. The links below go into more depth on how this is done. Instead of an waveform generator, the DMMs usually have a simpler circuit (usually only generating one or a few frequencies). Instead of an oscilloscope circuits that measure phase and amplitude to do the calculations.
The cool thing is, if you have an oscilloscope and waveform generator, you can also measure capacitance, sometimes better than a DMM. This also works for inductance to.
Edit: The high impedance is only for the voltage measurement setting. The impedance is much much lower when measuring capacitance.
According to Fluke:
A multimeter determines capacitance by charging a capacitor with a known current, measuring the resulting voltage, then calculating the capacitance.
They are not waiting for the RC time constant. It applies a known current for a certain time and looks at the ΔV. They may also do the same thing discharging the cap, in a loop.
Higher ΔV means lower capacitance.
Measuring a value of 1 Farad in 1 second with a DMM 1% resolution of 0.1mV and a measured value of 10 mV requires battery current when using pulse measurement techniques.
Even though RLC meters use a more precise constant current sinewave at selected frequencies to measure voltage amplitude and phase shift to compute all values, they still do not go up to 1 Farad.
Ic=CdV/dt= 1F * 10mV/1s = 10 mA which is more current than the DMM normally draws and would reduce battery life. So the Fluke 115 only measures up to 9999 uF.
The Keysight portable meters measure only up to 199.99 mF 
However, if you follow Maxwell's ultracap test procedure, you won't need a $1k+ rack mount RLC meter that does offer 1F readings.
But it does take more than 1 second.
