A rotor catch assembly includes a rotor catch housing and a rotor catch stem. The rotor catch housing is tubular and includes a landing ring formed on an inner surface thereof. The rotor catch stem is tubular and includes an annular landing flange about the rotor catch stem. The landing flange is positioned within the bore of the rotor catch housing above the landing ring. The interior of the rotor catch stem defines a rotor catch stem bore, which is coupled to the bore of the rotor catch housing below the landing ring by a rotor catch nozzle. The rotor catch stem includes a piston assembly, burst disk assembly, or nozzle assembly positioned to reduce or stop flow through the rotor catch stem bore through the rotor catch nozzle until the landing flange of the rotor catch stem lands on the landing ring of the rotor catch housing.