David,
If you have a 100 MHz oscillator, it will produce localized radio waves at 100 MHz when it oscillates. When you connect the oscillator on a breadboard, you are using relatively long wires. These wires are acting as an antenna. I assume that you have a radio receiver nearby that you are using to detect the radio waves.
You can't really prevent the circuit from producing radio waves but what you can and should do is to reduce the size of the radio waves to where they can't be picked up unless you attach an antenna.
The best way to start with that is to make the wires in your oscillator circuit as short as possible. If that doesn't work you may have to put a shield around the circuit.
It's likely that by building the circuit on a perfboard using the shortest connections you can, you will reduce the radio waves to not be detectable without an antenna.