The problem

The problem I had was: What do I do with all the "useless" rolls?

Other answers on this question attempt to give these useless rolls a not-so-useless purpose. My answer attempts to help you reduce the rolls which you think are useless.

The useless rolls are a result of the players picking up the dice and start rolling for checks that weren't called for. As the Game Master, you are the adjudicator. That means that you decide if the intention of the players must be randomly determined through the use of dice.

As you are all new to table top RPGs, it's possible that there is the idea within your group that all actions must be determined through the use of dice. Pathfinder is a very mechanical RPG, and has a rule or throw of the dice for most things you can think of. But it's not true that you have to roll for everything.

The fact you labeled the rolls "useless" is an indication to me that you want to avoid these rolls, as you're getting to the point where you have to keep saying there is nothing of interest in the room. Again, other answers try to give new purpose to those rolls, but I'll go into how you could avoid having these rolls in the first place.

The style of play I am about to describe is one of the methods you can play the game and mix fiction with mechanics. This is only one ethos of many you can follow to play the game, and it has really worked well for me in my campaigns.

Adjudicating actions differently to reduce the number of useless rolls

To address your problems of having too many "useless" rolls, let's look at how we can reduce rolling in the first place. Consider letting the players only do one of the following things:

• ask a question about the game world, or;
• state their intended action(s) and their approach.

Doing this, players don't state the skill they want to use for a given situation, they state their intentions. As the Game Master, you know how that intended action can be adjudicated, and you can (or not!) request the player to make a Perception / Diplomacy / Bluff / Whatever skill check.

They used to state

I want to roll a Perception Check to look around the room.
I want to roll a Diplomacy Check to tell the guard to calm down.
I want to roll a Stealth Check to sneak past the sentry with these clothes I found.

Now they'd state

I want to look around the room. What do I see?
I want to unsheathe my sword and tell the guard to calm down.
I want to use the clothes I found to sneak past the sentry.

When a player has stated their intention and approach, ask yourself the following questions:

1. Is the action possible? Does their approach actually bring about their intention? If you determine the action is not possible, the action fails and you do not require a die roll.
2. Do I need to use the game mechanics to figure out what happens? If the action can't actually fail or failure is extremely unlikely, the action succeeds and you do not require a die roll. If the action can fail, but failure carries no risk or cost and the player can freely try again and again, the action succeeds. But, if the action can fail and failure somehow changes the characters' situation, you need to use the dice.
3. How do I determine random success? The player's stated approach should clue you in to which ability score, skill, attribute or ability should be used to determine success. This is the part where you crack the book and roll the dice.

You see a mural that depicts the battle of your ancestors. [You roll Perception Check behind screen, succeeds] You also see a key lodged between two bricks in the wall.
You pull out your sword and tell off the guard. Roll for an Intimidate Check Initiative.
You put on the clothes you found in an attempt to blend in with the crowd. Roll a Disguise Check.

4. How do I describe the result? By letting the players state their intention, you know what success looks like.

Players are focused on what they are good at

Note how in step 3, you asked the player to roll a different skill than what they stated. Players often look at their character sheets, find a skill that is highly trained and try to use that over something else. They might try to use Acrobatics instead of Climb, or Intimidate instead of Bluff. By making it a rule of thumb that they are not allowed to ask for skill checks, and only state intentions or ask you questions about the in-game world, you can (or not!) ask them for a skill check. This can eliminate a lot of "useless" rolls.

The Angry DM has a very good article on adjudicating actions. It has helped me with situations like this.

A parting thought

The main reason to keep the crunching with the GM and the fiction with the players for me was that, in the end, it's going to be the GM's call. By avoiding to create 'rules lawyers' and keeping them focused on describing their intentions and approach rather than zoom in on one of their skills I think I have made the games I ran more fluid and fun. However, this policy is a mixed bag, and you'd be wise to find out for yourself if this policy works for your group. It may not directly answer your specific question about the Perception roll, but it could solve the root problem in the long term.