What is the proper way to do this, considering the reflections?
if you are using a normal 10:1 probe there shouldn't be any. depending on the frequency, you may have some capacitive loading from the probe. with a 10:1 probe you are placing an 11 Meg load (plus a small capacitive load) on the circuit. there's not enough current through the probe to get "reflections" unless you are are working somewhere north of 300Mhz. some test instruments do have a 50 ohm termination at the input, and they are calibrated with that load in place, but you wouldn't normally use an oscope probe with those inputs.
if you are just poking around inside a receiver for troubleshooting, all that really matters is that you can see the signals. you don't usually need a whole lot of accuracy, you're looking to see if a signal was amplified or attenuated, or is missing altogether. you're looking at the output of the local oscillator, and the output of the mixer to find out if the original RF signal has been converted to the intermediate frequency, and is passing through to the detector, and finally looking at the audio waveform after the detector. you don't need more than one decimal place of precision, and most of the time not even that, it's "did the signal get bigger, smaller, or disappear?"
Doesn't the 10x probe have to be terminated too?
Even if it is probing a 50 ohm resistor, the signal travels through the 10x probe cable (from the tip to the BNC connector on the scope).
If the 10x probe cable is 1 meter, and the signal is 60 MHz (5 m wavelength), wouldn't there be trouble?
the 10X scope probe is terminated with 1 Meg at the scope. since there's such a large resistance present, even if the probe coax were to be at the proper length to have problems with standing waves, the resistances are so high that the resonant circuit formed by the capacitance and inductance in the cable has very nearly a "Q" of zero. any tendency of the cable to act as a resonator is quashed by the 1 Meg termination. it's like putting a wet blanket on a tuning fork.
this
LTC application note has a lot of good information about making RF measurements. there are some real gems in the appendices, primarily Appendix A, which is a tektronix application note about ho oscope probes work. i really think that particular article should be recommended reading for anybody buying their first oscope.