How to measure the impedance of PCB trace
Unless you want to do your own S-Parameter de-embedding mathematics, you must fit a 50\$\Omega\$ connector to at least one end of the trace. You can either fit a connector to the other end, or a good quality 50\$\Omega\$ resistor. I tend to use 2 x 100\$\Omega\$ resistors in parallel for lower ground inductance.

There are many connector styles to choose from, you just haven't looked hard enough yet. If you are only going to 1GHz, then the tolerances will be fairly pedestrian. 

If you have a pattern of vias at the end of the trace, you should be able to find a connector with a through hole spill pattern that fits. If not, drill holes adjacent to the signal via through the ground plane to take the grounding spills of such a connector.

If you only want to measure the trace, and not the via, then you have more options. There are many connectors designed to fit a board edge. Cut the via off the board, and fit the connector to the end of the trace at the board edge.

You can solder 50\$\Omega\$ coax to the end of the strip, but you will need to be careful of excess lengths, same pedestrian tolerances but easier to get wrong with cable. Don't tell my boss, but often I would cut a lab 50\$\Omega\$ connectered cable in half, and solder each bit to my test board, saves fitting connectors to cable!

Equipment. A Time Domain Reflectometer (TDR) will give you a nice graphical display of impedance versus distance. A Network Analyser will give you traces of S-Parameters versus frequency, which you would need to analyse to determine the impedances you have. Hint, in the bad old days, a TDR did actually throw a pulse down the track and listened for the reflections. These days a TDR is simply a Network Analyser with an FFT function to synthesise the effect of such a pulse. Both of these types of equipment are very expensive, even to hire for short periods.

There are plenty of ways you can rig cheaper equipment, and some thought, into making measurements of impedance, even if not to 1GHz. A good logic source and a fast digital 'scope will get you a 'poor man's TDR'. A signal generator, a measuring receiver (a 'scope, a power meter, a spectrum analyser), and several tapping points for resistors and a bit more thought will allow good impedance measurements over the frequency range of your source and receiver.