When there are two integrated circuits clocked on the same frequency it should be possible clock both ICs from a single oscillator. My understanding is that the first chip is connected to the external circuitry (crystal or resonator) as usually via two pins - first is output from oscillator (inverting amplifier) that drives the crystal/resonator and second is input to the oscillator (feedback). The second chip has the oscillator output bypassed and only the input is connected to the crystal or resonator.
How can I verify that both ICs can be clocked reliably like this? What problems might arise?