  A concrete and experimentally feasible example for testing the putative
Majorana zero energy state bound in a vortex is theoretically proposed for a
parallel plate geometry of superfluid $^3$He-A phase. We examine the
experimental setup in connection with ongoing rotating cryostat experiments.
The theoretical analysis is based on the well-established Ginzburg--Landau
functional, supplemented by microscopic calculations of the Bogoliubov--de
Gennes equation, both of which allow the precise location of the parameter
regions of the Majorana state to be found in realistic situations.
