  $^3$He is an example of the system with non-trivial Cooper paring. A few
different superfluid phases are known in this system. Recently the new one, the
polar phase, have been observed in $^3$He confined in nematically ordered
aerogel. A number of various topological defects including half-quantum
vortices can exist the polar phase. In this work we present theoretical and
numerical studies of linear NMR in the polar phase both in the uniform
order-parameter texture and in the presence of half-quantum vortices.
