What do you expect to see?
If the scope is bright enough to display that extremely high frequency, it won't have an accurate amplitude because the 'scope's bandwidth is already rolling off, and the probe's capacitance is like a dead short at such a high frequency.
You won't see distortion nor clipping, because then you need a 'scope with at least a 10GHz bandwidth to show a few harmonics of 1GHz.
What produces your 1GHZ? Digital logic, microwave receiver or microwave transmitter?