An electric induction furnace for melting and holding a reactive metal or alloy is provided with an upper furnace vessel, an induction coil positioned below the upper furnace vessel, and a melt-containing vessel positioned inside the induction coil with a gap between the outside surface of the melt-containing vessel and the inside surface of the induction coil that can be used to circulate a cooling fluid for cooling the wall of the melt-containing vessel to inhibit leakage of the reactive metal or alloy melt from the vessel. The melt-containing vessel can be integrated with a cooling system for cooling the melt-containing vessel. The melt-containing vessel, induction coil and cooling system can be provided as modular components to facilitate servicing of the melt-containing vessel, the induction coil and the cooling system.