So I'm a big believer that you can do one thing well. If you are focused on sneaking about you can not also be focused on searching out for hidden enemies. The most likely outcome when you have two groups focused on not being noticed is they pass each other like ships in the night. They might notice each other passively, but generally only if someone rolls poorly.
One option would be to have more codified rules. Like, if you are trying to be sneaky and alert at the same time, disadvantage is applied to both rolls.
I'd rather not have a rule, though. Are there situations where one action makes another easier? Does this apply to any two tasks, or just sneaking and being alert? Is it specified as Stealth and Perception? Because players are supposed to declare actions, not skill use, how would that be phrased? "When the DM requires you to make simultaneous Stealth and Perception checks..."
Blah.
But this works great if we declare goal and approach, and DM adjudicates.
"I'm going to try to slip through the crowd unnoticed, while keeping an eye out to see if anybody suspicious is watching the bridge."
"How are you trying to be unnoticed?"
"I'll keep my eyes down and try not to make eye contact with people?"
"You can't really do that and look around for suspicious people at the same time. I'll let you pick one or the other, otherwise you're not going to do either one very well."
"Fine, I'll look around."
"As you scan from one person to the next, your eyes meet those of somebody standing on the bridge. He stares straight at you."
"Oh crap. I'll casually let me eyes drift away and keep going, but try to watch him with my peripheral vision."
"That you can do. He leaves the bridge and is walking in a direction that will intercept yours. You seem him wave a hand, as if signalling to somebody."
"Crap crap crap. I'm going to try to move near a denser knot of people, then duck and see if I can slip away unseen."
"Toward the bridge, or away from it?"
"Away from it. I'll come back later with a different plan."
"Gimme a Dexterity check."
"Cool. Can I use my Stealth proficiency?"
"Yes, that seems appropriate."
EDIT:
Wait. I want to change that. (See, I need to practice...)
"Away from it. I'll come back later with a different plan."
"Ok, you find a knot of people and pull a slick move. A couple of passersby look at you funny, but if you stay low you can move between carts and groups of people and stuff toward an alley."
"Do they see me?"
"What do you do to find out?"
"I look back and....oh, wait, no. Crap. I head for an alley and duck in."
"It's a dead-end alley, with nothing in it."
"Oh no. I go to the end, put my back to the wall, and draw my sword."
"Oh, let's have a Dexterity roll to see if you escaped unseen."
"Can I use Stealth proficiency?"
"Definitely."