This paper is dedicated to the design of incomplete equations of state for a two-phase flow with phase transition that are specific to the low Mach number regime. It makes use of the fact that the thermodynamic pressure has small variations in this regime. These equations of state supplement the 2D LMNC model introduced in previous works. Our innovative strategy relies on tabulated values and is proven to satisfy crucial thermodynamic requirements such as positivity, monotonicity, continuity. In particular, saturation values are exact. This procedure is assessed by means of analytical steady solutions and comparisons with standard analytical equations of state, and shows a great improvement in accuracy.