You don't actually get a 4-vector for anything in particular. You get a 4-vector for the-sum-of-unobserved-stuff where the unobserved stuff may included neutrinos as well as any neutral beyond-the-standard-model things you could be searching for.
In an ideal world you would get this 4-vector by totaling up the detected particles and subtracting them from the total for the incident particles.
Alas, this is not a perfect world, and a lot of stuff is generally lost down the beam-pipes. That's why we restrict ourselves to the transverse observables. However, that means that the energy expected in the transverse channels is not simply given by the incident particles.
I'm not sure where they usually go from there (not doing collider physics), but you do know that the expected, total transverse momentum is zero, and that means you can find the missing transverse momentum. If you then assume a mass for the unobserved particle (perhaps having chosen events for which there is no obvious source of neutrinos), you can then figure the energy.