Instrumentation of higher order modes (HOMs) excited in accelerating cavities for beam phase and position inference provides a noninvasive and economical beam diagnostic. The principles and techniques for this purpose are investigated for TESLA (TeV Energy Superconducting Linear Accelerator) cavities at the injector part of the newly built European XFEL and at FLASH, two free electron laser facilities based on the TESLA technology. I have designed and instrumented unconventional beam phase monitors based on monopole modes in TESLA cavities and demonstrated a routine resolution of 0.1 degrees with a broadband setup. The best resolution achieved with this system is 0.03 degrees. The resolution is largely limited by the signal power. In order to aid the monitor design and study its performance, I have employed a coupled circuit model which indicates that the resolution can be further improved by optimizing the SNR (signal to noise ratio) and sampling frequency. This is the first type of monitor that is able to probe online the beam phase directly w.r.t. the accelerating field in individual accelerating cavities. The system can be used for long term RF drifts monitoring and also be used to decouple the phase jitter and drift sources in the injector part of a linac. Therefore the system can provide valuable information for the low level RF system. Beam position monitoring based on dipole modes in TESLA cavities at FLASH was demonstrated for the first time to work stably over several months with below 5 micrometers resolution. The improvement is attributed to a focused campaign on various signal and analysis techniques. These techniques can be transferred with little effort to the similar system, now under design for the European XFEL. As a preparation for the beam position monitor for the third harmonic cavities at the E-XFEL, I have measured and characterized the HOM spectra for single and coupled cavities. In particular there existed no such measurements for eight coupled cavities. These measurements pave the way for the instrumentation of 3.9 GHz cavities and show that the modes are well damped to the required limit.