  We employ a variety of symmetry breaking patterns in $SO(10)$ and $E_6$ Grand
Unified Theories to demonstrate the appearance of topological defects including
magnetic monopoles, strings, and necklaces. We show that independent of the
symmetry breaking pattern, a topologically stable superheavy monopole carrying
a single unit of Dirac charge as well as color magnetic charge is always
present. Lighter intermediate mass topologically stable monopoles carrying two
or three quanta of Dirac charge can appear in $SO(10)$ and $E_6$ models
respectively. These lighter monopoles as well as topologically stable
intermediate scale strings can survive an inflationary epoch. We also show the
appearance of a novel necklace configuration in $SO(10)$ broken to the Standard
Model via $SU(4)_c\times SU(2)_L\times SU(2)_R$. It consists of $SU(4)_c$ and
$SU(2)_R$ monopoles connected by flux tubes. Necklaces consisting of monopoles
and antimonopoles joined together by flux tubes are also identified. Even in
the absence of topologically stable strings, a monopole-string system can
temporarily appear. This system decays by emitting gravity waves and we provide
an example in which the spectrum of these waves is strongly peaked around
$10^{-4}~{\rm Hz}$ with $\Omega_{\rm gw}h^2\simeq 10^{-12}$. This spectrum
should be within the detection capability of LISA.
