  A reliable model order reduction process for parametric analysis in
electromagnetics is detailed. Special emphasis is placed on certifying the
accuracy of the reduced-order model. For this purpose, a sharp state error
estimator is proposed. Standard a posteriori state error estimation for model
order reduction relies on the inf-sup constant. For parametric systems, the
inf-sup constant is parameter-dependent. The a posteriori error estimation for
systems with very small or vanishing inf-sup constant poses a challenge, since
it is inversely proportional to the inf-sup constant, resulting in rather
useless, overly pessimistic error estimators. Such systems appear in
electromagnetics since the inf-sup constant values are close to zero at points
close to resonant frequencies, where they eventually vanish. We propose a novel
a posteriori state error estimator which avoids the calculation of the inf-sup
constant. The proposed state error estimator is compared with the standard
error estimator and a recently proposed one in the literature. It is shown that
our proposed error estimator outperforms both existing estimators. Numerical
experiments are performed on real-life microwave devices such as narrowband and
wideband antennas, two types of dielectric resonator filters as well as a
dual-mode waveguide filter. These examples show the capabilities and efficiency
of the proposed methodology.
