Tidal flow of seawater across the Earth's magnetic field induces electric currents and magnetic fields within the ocean and solid Earth. The amplitude and phase of the induced fields depends on electrical properties of both the seawater and the solid Earth, thus can be used as a proxy to study seabed properties or potentially for monitoring long-term trends in the global ocean climatology. This paper presents new global oceanic tidal magnetic field models and their uncertainties for four tidal constituents, including $M_2, N_2, O_1$ and $Q_1$, which was not reliably retrieved previously. Models are obtained through a robust least-squares analysis of magnetic field observations from the \textit{Swarm} and CHAMP satellites using a specially designed data selection scheme. We compare the retrieved magnetic signals with several alternative models reported in the literature. Additionally, we validate them using a series of high-resolution global 3-D electromagnetic simulations and place constraints on the conductivity of sub-oceanic mantle for all tidal constituents, revealing an excellent agreement between all tidal constituents and the oceanic upper mantle structure.