I missed the 'microwave part'.

Physics is the science that explains a phenomenon - engineering is putting the phenomenom to use. You want an engineering technique to solve a problem that physics has already described.

Phase is one means of measuring time of flight. If the target is moving you will have the Doppler effect changing the return frequency, so phase alone may not be useful.

So is your target moving or stationary?

Laser rangefinders use the technique of 'undersampling' whereby the time difference between the send and receive pulses is warped down to microseconds rather than picoseconds. This relies on the send pulses being regular. This would work for microwave also. The technique is akin to sampling a regular signal at less than its frequency. Like having a digital scope with 1msps and feeding it a 10mhz sinewave. You will see a sinewave, but its frequency is much lower than the input signal. That's how it was explained to me. The circuitry i've seen uses a little 'f' series ttl and a 80c51fa and gives centimetre accuracy.