Sweep Frequency Response (SFR) measurement on a transformer is a low voltage, offline exercise. So, it virtually permits determination of any network or system function, by imposing any desired terminal condition for the nontested windings and terminals. The terminal conditions employed have significant influence on the achievable fault detection ability, and maximizing this ability should obviously be one of the main aims of frequency response measurements. Simply stated, this requirement translates to the ability to identify/measure as many natural frequencies as possible. However, there is a practical limitation that not all system functions can exhibit all natural frequencies. Hence, it is necessary to determine the most appropriate combination of terminal connection and system function for achieving this objective. The growing popularity of SFR measurements has led to a new IEEE Guide. This document (IEEE Std PC57.149TM/D1) on SFR measurement lists out most of the possible terminal connections and system functions, for both 1φ and 3φ transformers. Surprisingly, it does not identify and recommend any one of them as preferred for maximizing this objective. Initially, considering the high frequency equivalent circuit representation of a 1φ, twowinding transformer, system function for different terminal conditions were computed. Depending on the number of natural frequencies distinguishable in the amplitude frequency response of a system function, each measuring condition was ranked. Thus, it led to identification of the best configuration. Later, these findings were verified on an actual 1φ, two-winding transformer. However, 3φ transformers are quite different in construction compared to 1φ transformers. So, whether the same configuration would also be applicable for SFR measurements on 3φ transformers had to be ascertained. So, the study was next extended to 3φ transformers. Performance of best configuration identified during this investigation are compared with currently employed low-voltage impulse test (used during short-circuit testing of transformers) and currently practiced SFR measurement test conditions, and found to be better. In conclusion, it is believed that after adequate field verifications, the identified configuration can be declared as the preferred way of making SFR measurement on transformers.