We investigate the large order aspects of the delta expansion under the estimation procession of the critical quantities. As illustrative examples, we revisit the one-dimensional Ising model for the analytic study and the two-dimensional square Ising model in the high-temperature phase for the numerical experiment to large orders. In both models, the proposed fundamental base on which the estimation protocol should be constructed is investigated in detail and confirmed to be valid. In the square lattice model, we present a new protocol for the estimation of critical exponents and temperature.