  Planar superconducting microwave transmission line resonators can be operated
at multiple harmonic resonance frequencies. This allows covering wide spectral
regimes with high sensitivity, as it is desired e.g. for cryogenic microwave
spectroscopy. A common complication of such experiments is the presence of
undesired 'spurious' additional resonances, which are due to standing waves
within the resonator substrate or housing box. Identifying the nature of
individual resonances ('designed' vs. 'spurious') can become challenging for
higher frequencies or if elements with unknown material properties are
included, as is common for microwave spectroscopy. Here we discuss various
experimental strategies to distinguish designed and spurious modes in coplanar
superconducting resonators that are operated in a broad frequency range up to
20 GHz. These strategies include tracking resonance evolution as a function of
temperature, magnetic field, and microwave power. We also demonstrate that
local modification of the resonator, by applying minute amounts of dielectric
or ESR-active materials, lead to characteristic signatures in the various
resonance modes, depending on the local strength of the electric or magnetic
microwave fields.
