During certain medical procedures, it is important to continuously measure the respiratory flow of a patient, as lack of proper ventilation can cause brain damage and ultimately death. The monitoring of the ventilatory condition of a patient is usually performed with the aid of flowmeters. However, water and other secretions present in the expired air can build up and ultimately block a traditional, restriction-based flowmeter; by using an orifice plate flowmeter, such blockages are minimized. This paper describes the design of an orifice plate flowmetering system including, especially, a description of the numerical and computational techniques adopted in order to simulate human respiratory and sinusoidal air flow across various possible designs for the orifice plate flowmeter device. Parallel computation and multigrid techniques were employed in order to reduce execution time. The simulated orifice plate was later built and tested under unsteady sinusoidal flows. Experimental tests show reasonable agreement with the numerical simulation, thereby reinforcing the general hypothesis that computational exploration of the design space is sufficiently accurate to allow designers of such systems to use this in preference to the more traditional, mechanical prototyping techniques.