We calculate the factor by which thermal phase fluctuations, as distinct from phase-slip fluctuations, increase the inductance, LJ, of a resistively-shunted Josephson junction (JJ) above its mean-field value, L0. We find that quantum mechanics suppresses fluctuations when T drops below a temperature, TQ = h/kBGL0, where G is the shunt conductance. Examination of the calculated sheet inductance, LA(T)/L0(T), of arrays of JJ's reveals that 2-D interconnections halve fluctuation effects, while

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... cing phase-slip effects by a much larger factor. Guided by these results, we calculate the sheet inductance, LF(T)/L0(T), of 2-D films by treating each plasma oscillation mode as an overdamped JJ. In disordered s-wave superconductors, quantum suppression is important for LF(0)/LF(T) > 0.14, (or, T/TC0 < 0.94). In optimally doped YBCO and BSCCO quantum suppression is important for l2(0)/l2(T) > 0.25, where l is the penetration depth.