Phase Response Measurement
You use an oscilloscope, with inputs for both the input and output of the block you need the phase response for to measure the time difference between peaks of the input and peaks of the output for input sine waves of various frequencies.  Then, multiply time delay divided by the period by 360 deg/cylcle to get the phase in degrees.

Many scopes, even inexpensive scopes, let you use averaging to get better measurements in the presence of noisy inputs and outputs.  You can also adjust scope sensitivity and the time base to let you capture the most accuracy in your measurement. For that matter, many scopes these days have a phase measurement option in their measurement menu.