B757 pilot reported a 'Cabin Altitude High' EICAS message and master warning during cruise flight. Crew performed checklist procedures; continued to destination and landed normally.

Narrative

Operating Aircraft X maintenance ferry from ZZZ1 to ZZZ. We prepared the aircraft via the ACARS inop checklist and departed ZZZ1. Just beyond halfway through the flight; we encountered turbulent rides at Flight Level 300. At which point we requested a climb to 360. Shortly thereafter the request was approved At which point we climbed to 360. Close to 15 to 20 minutes after being at Flight Level 360 we were notified by a cabin altitude high EICAS message and Master warning chimes. At which point the Captain and I conducted our memory items for the cabin altitude high QRC checklist. The Captain delegated the checklist to me; and he assumed the role of Pilot Flying and radio operation. I Conducted the checklist items while the Captain notified ATC. After verifying on the panel that the cabin altitude was high; we began our descent from 360 down to 10;000 feet. I completed the QRC actions in full; and Once level at 10;000 feet; the Captain and I Consulted with each other; and then with Dispatch at which point; we decided to continue to ZZZ being that the aircraft was stable and safe to continue operating. The Captain maintained operation over the flight controls and the radios while I set up for the approach and briefed the Arrival into ZZZ. After my briefing was complete; I was given back operation of the flight controls and the Captain resumed Pilot Monitoring duties. We conducted a Visual approach; backed up by an ILS to Runway XXR into ZZZ; Landed the aircraft safely and taxied to the gate without the need for emergency vehicles or assistance. We then thoroughly debriefed the flight and its event together; and departed the aircraft.