Here is how to check your work for this example.
Design your microstrip transmission line. Make it longer than 1/4 wavelength. Plot the S11 on a 50 ohm Smith chart starting at zero Hertz and make a note when the spiral 1st crosses the real axis on the Smith chart. Calculate the reflection coefficient at this point. It will be a real number but the sign may be + or - depending on the angle being 0 or 180 degrees. Calculate the actual line impedance using this formula:
Zline = (50 ohms)*square_root[ (1+reflex)/(1-reflex) ]
To check this, I designed a microstrip 100 ohms, 135 degrees long @ 1GHz. It 1st crossed the real axis at 670 MHz, Z=192.3 ohms. Reflection coefficient calculates to 0.5873 @ 0 degrees.
Zline = (50 ohms)*square_root[ (1+0.5873)/(1-0.5873) ]
Zline = 98.06 ohms
This is also the way to check actual transmission lines using a network analyzer.