Each Ordinatus was unique, and in the game's background, could only be sanctioned by the Centurio Ordinatus. They generally appear as a huge tracked vehicle, as large as a building, with a massive weapon system mounted on top. Individual Ordinatus machines were constructed for a sole, original purpose for a particular battle. This is why the different Ordinatii have very specialized weapon loadouts configured for their intended role. According to the background information, only a few of the machines were actually built, and each was named for the specific planet upon which it was built.
Armed with a ferocious Nova Cannon, Ordinatus Armageddon was originally constructed for the first battle of Armageddon, against the forces of Chaos. Background-wise, this machine was constructed to take on and destroy enemy Titans head-on with its Nova Cannon. A metal miniature of this war machine was released in 1995. During the Third War for Armageddon, the Ordinatus Armageddon destroyed the Ork Great Gargant Skullsmasha at Sreya Rock.
Ordinatus Golgotha was an Ordinatus armed with eight, massive Hellfire missiles mounted in a battery on the surface of the machine. Background-wise, it was constructed for combat on the Squat homeworld of Golgotha. Along with Ordinatus Armageddon, this machine received a metal miniature released by Games Workshop.
During the Horus Heresy, even the Adeptus Mechanicus planet of Mars was in a state of rebellion. One of the first to be constructed, Ordinatus Mars was created during this time to break through the defenses of the rebels holding up in the city of Castellum Jericho. The Ordinatus was armed with a massive Sonic Disruptor, which was well-suited for bringing down even the reinforced walls of the city. This massive siege engine was one of three Ordinatii to have metal miniatures made of them, along with Armageddon and Golgotha.
The Ordinatus Priam was a huge machine equipped with various drilling and digging implements. It was originally designed to travel through a planet's mantle in order to bypass the defenses of the city of Priam. No model was ever released for this particular machine and it was mentioned in the Ordinatus article only in passing.
Unnamed Ordinatus on Volcanis Ultor: Mentioned only in passing in the novel "Grey Knights" This Ordinatus was intended to destroy the Grey Knights before they could manage to breach the defense lines. However, this Ordinatus is destroyed by the wreckage of the Grey Knights strike cruiser, Rubicon, after it was destroyed by the ships defending the planet from space, crashed into the defense lines.