We discuss the expected performances of ultracryogenic, T=100 mK, resonant, nu =1 KHz, gravitational wave antennae, with reference to the antenna AURIGA. The detector sensitivity is numerically calculated and optimized with respect to the matching parameters of the electromechanical transducer chain. Other parameters, such as the electrical and mechanical Q--factor, the SQUID energy resolution, the electrical coupling factors, etc. are set at values achieved in separate tests. The predicted optimal sensitivity to impulsive gravitational wave signals is hmin = 8 x10-20 with an optimal post detection bandwidth of 50 Hz. The data acquisition and analysis allow storage of uncompressed data and determination of burst arrival times. A minimal network of six resonant antennae, three pairs in three sites, would allow unambiguous reconstruction of the incoming g.w. burst.
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