Let U σ 2n be the set of unicyclic signed graphs with perfect matchings having 2n vertices, where σ is a signing function from the edge set of the graphs considered to {−1, 1}. The increasing order of the signed graphs among U σ 2n according to their minimal energies is considered. A relationship between the energies of a unicyclic graph and of its signed graphs is derived. A new integral formula for comparing the energies of two signed graph is introduced. In U σ 2n with n ≥ 721, the first 18 signed graphs in the increasing order by their minimal energies are obtained