Testing Oscillator Over Temperature
the oscillator is designed to drive a high-impedance IC clock input


In this case, you will want to add a buffer chip to be able to drive the 50 Ohm coax and the spectrum analyzer input. The appropriate chip depends on what type of load the oscillator is designed to drive (TTL, CMOS, ...?), the frequency, the available power supply voltages, etc. 

Possibly you could use a transformer instead of an IC buffer to impedance-match the cable, but the buffer has the advantage of providing exactly the type of load the oscillator is designed for (an IC input).

Incidentally, if you want to measure the frequency accuracy of your oscillator and not other parameters, a frequency counter will give you a more accurate measurement more quickly than a spectrum analyzer. But it will still likely have a 50 Ohm input unless you're working at very low frequencies (below 1 MHz?).