So my friends Ed and Steve and I were hanging out at his place this evening, when Ed gets a call from St. Luke's hospital, telling him his mother passed out and was taken to the emergency ward. So all three of us drove over to Bethlehem to make sure she was alright. All three of us carry pretty much all the time.
In this particular scenario, Steve was wearing a suit and had a 1911 concealed under his suit jacket. Ed was wearing an untucked white button down shirt, concealing his XD. I, on the other hand, was openly carrying my SW99 on my belt, wearing slacks and a tucked-in gray button down shirt. So we walk into the waiting room, and all take adjacent seats across from where the vending machines are. I got up to grab a cherry coke from the vending machine, went back to sit down. About five minutes later, two gentlemen walk out into the waiting area, making a beeline for the three of us. He asked me if I'd like to step outside or into the vending machine corridor (which is somewhat segregated from the rest of the waiting area), and I said sure.
We walked over and he said "we noticed on the security camera that you're carrying a firearm."
I responded with "Of course," since I was open carrying.
"Are you a law enforcement officer?"
"Not that I know of."
"Well, unfortunately this is private property, and the hospital has a 'no firearms' policy, in order to ensure the safety of our patients and employees."
"I see."
"So, we're going to have to ask you to either leave, or store your firearm in your car during your visit."
"..Ok..." I'm deliberating whether I want to come back at this point.
"I'm really sorry, sir, I understand where you're coming from. I carry all the time when I'm not at work, but the hospital makes the policies, not us."
"Well, it's certainly within the property owner's rights to ask me to leave, so I will."
I shook his hand and introduced myself, and he to me. Then Ed and Steve walked over into the vending area, Ed gave Steve his sidearm, and both Steve and I walked out to store the weapons in my car (Ed had his 8 month old son with him, so he couldn't leave him to go disarm). After securing the weapons in the car, I came back, since I couldn't very well leave Ed defenseless after he left. I kept my empty holster on my belt. No further issues this evening.
While I'm disappointed in the hospital's decision to disarm its visitors, I'm glad to report that the security staff was very attentive, and that they were also polite and personable.
Any other seasoned open carriers who wish to chime in on what I did right, what I did wrong, and what they would have done differently, are certainly welcome.

Bear in mind, that there are no signs anywhere that state any 'no firearms' policy on this premises.
ETA: Ed's mom is fine, she passed out due to a very low potassium level, which creates heart palpitations. She's on a potassium feed, and will probably be out tomorrow. She hadn't eaten anything in a couple of days due to lack of appetite, but she should be fine now.