This paper describes an interferometric pressure sensor designed to work as a remote sensor in a coherence modulation scheme, allowing a linear phase read-out of the signal. The sensor is realized from a silicon nitride waveguide Mach-Zehnder interferometer integrated on a (100) silicon substrate, and includes a micromachined membrane below a branch of the Mach-Zehnder. The characterization is achieved by a spectral analysis and shows a nonlinear relationship between the static pressure applied to the membrane and the phase variation thus obtained. The analytical description takes into account the induced deflection of the membrane and the resulting mechanical elongation of the waveguide.