  Remnant radio galaxies represent an important phase in the life-cycle of
radio active galactic nuclei. It is suggested that in this phase, the jets have
switched off and the extended emission is fading rapidly. This phase is not
well-studied due to the lack of statistical samples observed at both low and
high frequencies. In this work, we study a sample of 23 candidate remnant radio
galaxies previously selected using the Low Frequency Array at 150 MHz in the
Lockman Hole field. We examine their morphologies and study their spectral
properties to confirm their remnant nature and revise the morphological and
spectral criteria used to define the initial sample. We present new
observations with the Karl G. Jansky Very Large Array at 6000 MHz at both high
and low resolution. These observations allowed us to observe the presence or
absence of cores and study the spectral curvature and steepness of the spectra
of the total emission expected at these high frequencies for the remnant
candidates. We confirm 13 out of 23 candidates as remnant radio sources. This
corresponds to 7% of the full sample of active, restarted, and remnant
candidates from the Lockman Hole field. Surprisingly, only a minority of
remnants reside in a cluster (23%). The remnant radio galaxies show a range of
properties and morphologies. The majority do not show detection of the core at
6000 MHz and their extended emission often shows ultra-steep spectra (USS).
However, there are also remnants with USS total emission and a detection of the
core at 6000 MHz, possibly indicating a variety of evolutionary stages in the
remnant phase. We confirm the importance of the combination of morphological
and spectral criteria and this needs to be taken into consideration when
selecting a sample of remnant radio sources.
