It is well established that concrete durability strongly depends on the capillary porosity of the material. Hence, structural health monitoring of concrete structure could take advantage of concrete microporosity monitoring. To this end, a new method for the in situ non-destructive testing of capillary porosity in cementitious materials has been proposed. A sensing device that seems well suited to this application is a capacitive ultrasonic transducer with a characteristic size of 1 \mum. It is to be embedded in the material. Its vibrating membrane is made of aligned carbon nanotubes forming a thin layer with a typical thickness of 1 nm. It generates acoustic waves of micrometric wavelength into water-filled micropores, aiming at measuring their properties.The present paper focuses on the numerical simulation of the embedded sensor. In order to properly account for viscous effects in fluids at the micrometric scale, we have developed a specific computational method for the visco-acoustic modelling of a microplate vibrating between 10 MHz and 2 GHz in a water-filled domain of micrometric size. Our approach is based on the condensation of the fluid part of the fluid-structure problem on the structure by a finite element method, and on a spectral approximation of the structural equations.The numerical results indicate that the fluid domain is resonant despite the viscous terms, which causes a frequency downshift of the resonances and a decrease of the quality factor. In the coupled system, the plate does not perturb the fluid resonances, whereas the plate resonances are strongly upshifted by the water load. The resonance frequencies of the system are shown to display a clear dependence on the pore width, which makes the device a good candidate as a porosity sensor.