Innovative high-frequency magnetic sensors have been designed and manufactured in-house for installation on the Tokamak a Configuration Variable (TCV), which are now routinely operational during the TCV experimental campaigns. These sensors combine the Low Temperature Co-fired Ceramic (LTCC) and the classical thick-film technologies and are in various aspects similar to the majority of the in-vessel inductive magnetic sensors foreseen for ITER (around 450 out of the 505 currently being procured are of the LTCC-1D type). The TCV LTCC-3D magnetic sensors provide measurements in the frequency range up to 1 MHz of the perturbations to the wall-aligned toroidal (delta B-TOR), vertical (delta B-VER), and radial (delta B-RAD) magnetic field components. Knowledge of the equilibrium at the last closed flux-surface allows us to then obtain the field-aligned parallel (delta B-PAR similar to delta B-TOR), poloidal (delta B-POL), and normal (delta B-NOR) components, the latter being in most cases rather different from the vertical and radial components, respectively. The main design principles were aimed at increasing the effective area and reducing the self-inductance of the sensor in each of the three measurement axes, which are centered at the same position on each sensor, while reducing the mutual and parasitic coupling between them by optimizing the on-board wiring. The physics requirements are set by the installation of two high-power/high-energy neutral beam injection systems on TCV, i.e., studying fast ions physics, coherent instabilities, and turbulence in the (super-)Alfvenic frequency range. In this paper, we report the manufacturing, installation, and commissioning work for these high-frequency LTCC-3D magnetic sensors and conclude with an overview of illustrative experimental results obtained with this system. The LTCC-3D data provide new insights into the delta B-POL coherent (eigenmodes, up to similar to 400 kHz) and in-coherent background turbulent fluctuations in the higher frequency range up to similar to 1 MHz, which were not previously available with the TCV Mirnov sensors. Furthermore, the LTCC-3D delta B-POL measurements allow us to cross-check the data obtained with the standard Mirnov coils and have led to the identification of largeelectromagnetic (EM) noise pick-up for the Mirnov data acquisition (DAQ). When the sources of EM noise pick-up on the Mirnov DAQ are removed, the LTCC-3D data for delta B-POL are in good overall agreement, i.e., within the expected measurement uncertainties, with those obtained with the standard Mirnov sensors located at the same poloidal position in the frequency range where the respective data acquisition overlap, routinely up to 125 kHz and up to 250 kHz in some discharges. The LTCC-3D delta B-PAR measurements (not previously available in TCV or elsewhere) provide evidence that certain instabilities have a finite parallel delta B at the wall, hence at the LCFS, consistent with the recent theoretical results for pressure-driven modes. The LTCC-3D delta B-NOR measurements improve significantly on the corresponding measurements with the saddle loops, which are mounted onto the wall and have a bandwidth of similar to 3 kHz (due to the wall penetration time). A detailed end-to-end system modeling tool has been developed and applied to test on the simulated data the actual measurement capabilities of this new diagnostic system and obtain the ensuing estimates of the intrinsic measurement uncertainties. A detailed error analysis is then performed so that, finally, fully calibrated, absolute measurements of the frequency-dependent amplitude and spectral breaks of coherent eigenmodes and in-coherent broadband magnetic fluctuations are provided for the first time in physical units with quantitative uncertainties.