Dorsey et al. [8] have constructed formal solutions for the half-space Ginzburg–Landau model, when κ is small. Dorsey et al. deduce a formal expansion for the superheating field in powers of κ½ up to order 4. In this paper, we show how the formal construction gives a natural way for constructing a subsolution for the Ginzburg–Landau system. We improve the result obtained by Bolley & Helffer [2], and take a step in the proof of the Parr Formula [13], getting two terms in the lower bound for the superheating field as κ → 0.