  Quantum models based on few-mode Master equations have been a central tool in
the study of resonator quantum electrodynamics, extending the seminal
single-mode Jaynes-Cummings model to include loss and multiple modes. Despite
their broad application range, previous approaches within this framework have
either relied on a Markov approximation or a fitting procedure. By combining
ideas from pseudomode and quasinormal mode theory, we develop a certification
criterion for multi-mode effects in lossy resonators. It is based on a witness
observable, and neither requires a fitting procedure nor a Markov
approximation. Using the resulting criterion, we demonstrate that such
multi-mode effects are important for understanding previous experiments in
X-ray cavity QED with M\"ossbauer nuclei and that they allow one to tune the
nuclear ensemble properties.
