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The energy states of a well-isolated hysteretic Josephson junction in the "phase" regime can be used as a qubit. The state of the junction can be determined by measuring when the junction switches from the zero-voltage (qubit) state to the running voltage state, since different levels have different switching rates. The experimental challenge is to provide sufficient electrical isolation of the junction from wires that must be attached to provide bias current and to measure switching events. This isolation must be effective at frequencies around the energy level spacing, in our case from 3-8 GHz. We report on the design and measurement of isolated moderate-to-high-Q junctions using a resonant isolation scheme of a series inductance and capacitive shunt. Microwave activation measurements of the Al-AlOx-Al junctions at 70 mK were used to gauge the isolation effectiveness and to show the effect of current noise from the isolation resonance on the junction coherence.