It is shown how complementary energy methods can be applied to problems involving the calculation of electrostatic fields. The results obtained using such methods provide error bounded solutions to the system energy, and may be compared with those found through application of the conventional finite element method. To illustrate the technique the classical problem of a cylindrical tank, half filled with a charged liquid, is investigated. Comparisons are made on the basis of computer C.P.U. time, and core storage requirements, for a given degree of accuracy in total system energy. The question of local error in primary field quantities is also examined.