Guaranteeing 100% absense means either physically blocking the room or removing the cats… so let's call this a 99% assurance.
Ssscat Pet Deterrent
I've had many many cats, and each of them insisted on being somewhere they did not belong. On the counter, in the garbage, digging in the pantry… this thing has stopped them all. It is not only an active repellent, but a training aid to teach them… never. to. return.
It is essentially a compressed air sprayer with a motion detector to activate it when someone gets too close. If a cat approaches, it makes a loud hiss and sprays a stream of air at the intruder. It's quite the deterrent — it almost kept me from using the counter when I got "caught" unexpectedly — but it is completely harmless to the cats and they'll quickly learn to stay away, even if you remove or turn the device off.
At $21.95, it sounds a bit expensive… but the "solution" is actually rarely used, and — bonus — you can re-deploy it at multiple locations throughout the house. One or two encounters with this thing is enough to keep even the most determined cats away from those compulsive areas they just have to explore. I tried for almost a year to keep my cats off the counter before I found this solution.
They don't go on the counter anymore.
And if I think they might try — think Thanksgiving turkey — leaving this on the counter (turned off, so I can approach without getting sprayed) is enough to assure the cats will not give in to that urge to explore.
For your situation, I would suggest placing this in front of the closed door facing outward into the hallway. They will learn quickly. Once they learn not to approach, I would try again with the door open. They will learn not to approach that room. I don't think it will take more than a few tries, but if you think they may forget their early lessons, you can leave the can on the floor (turned off, so you don't get psssssst'd every time you go into the room) as a reminder of what will happen if they approach. You don't even have to leave the can "on". The memory is enough to keep them away and, if they forget, the can is just a reminder.