There are many high frequency probes no doubt but they are expensive, really expensive.
Also, grounding is extremely important for a healthy measurement. You should consider grounding problem if you want to measure precisely.
Optimum option for such high frequency signals, is to use coaxial connectors such as BNC or SMA and to use 50 Ohm Input Impedance of the oscilloscope if it has. Otherwise the measurements will either be erroneous or noisy.
How clean do you want it? And how will you know that it's giving you signal accuracy?
Probes need their compensation tweaked to get best HF / transient fidelity. Then you need a reference signal. The front panel cal square wave is unlikely to be square at 1Ghz / 100ps/div.
I think your 1Ghz signal is going to be wrapped around a controlled-impedance line standard and if you're lucky Zo=50 and the termination is the scope input w/ termination set to 50.
For differential it's tougher but you can float the scope ground and tie to VTT, get matched cables and use vertical math to get the difference voltage displayed.
look out for aliasing
depending one the digitization rate, you may get an incorrect signal
some years back, i ran into this problem. 10 MHz looked like 1 Hz.
Very strange until we realized it was aliasing.
"Check clock" is rather unspecific. If you want check the signal quality of a 1 GHz square wave you need at least 5 GHz bandwidth. Presumed the signal can't be loaded with 50 ohm, a resistive passive probe, e.g. 20:1 with 1k input impedance, can be good solution.