TL;DR: My players have insane stats and constantly high rolls, and are going through content faster than I can churn it out.

My players are very nice, in addition to being invested in the game. However, four out of the six of them have insanely high rolls. (We also use the Honor Score)

EX:

Me: You see a trophy with your name on it. What do you do?

Rogue: I reach out to touch it.

Me: Make an Honor saving throw.

Rogue: Nat 20.

And so on and so forth. This doesn’t just happen in role-playing moments, it happens in combat, in contest checks, and literally anything you would roll the dice for. I’m good at making stuff on the fly, but this on level-not at all. Any ideas for how to keep them busy?

I'm not sure I fully understand the issue, but i'll try to offer suggestions.

Investigations - instead of challenges that can be decided by a single roll, introduce investigations where they have to collect clues and figure things out for themselves. Even better if the clues are spaced far apart (geographically which requires travel time and therefore multiple encounters, etc.).

Exploration - a large dungeon or set of ruins takes a bit of time to make, but a LOT longer to adequately explore.

Social encounters - they need to get info from several different people, each may be resistant and takes time to build their trust and multiple rolls.

If they have super high ability scores, put them up against super tough trap or challenge DCs (especially those that require multiple rolls to defeat).

The trophy is locked in a fancy display case made of a metal you don't recognize and thick crystal panes (highly resistant to damage). 

PC: I pick the lock (roll nat 20)

DM: Good job, you get a satisfying click as the tumblers click into place, but as you start to withdraw the pick, you feel resistance - a trap!

Now it takes a second roll to avoid the trap, which reveals a puzzle (combination lock) requiring the PC to figure it out, then the trophy sits itself might actually be a mimick... whatever. Multiple rolls to accomplish a task instead of just one.

How did you determine ability scores n the game? I'm not familiar with honor scores, but I'm going to assume if the problem is just the honor score you may need to reconsider how it is improved. 

If it's all the scores and you are high level , that's just high level. If you are low level, I might question whether the players are being honest with their roles. 

You'll need to come up with challenges that don't involve rolls

I think it would be a lot easier to offer something constructive if we knew a bit more - for example I play in a game where the stats are roll 4 d20 - 18+ is an 18 but generally players are allowed to reroll until they have a nice stat block 18/18/18/17/16/15 is not uncommon. This allows MAD classes to fully utilize all aspects of their class(s).

That said the DM understands that we are a group of seasoned players running around with high stat blocks, optimized gear and a fair bit of high end homebrew so at level 18 (Current level) it is not unusual to have creatures fighting us that have an ac of 26-28 - that hit for 50 points of damage per hit and get multi attacks and there will be a few of them in a fight. 

The fights are interesting there is almost always a range dps creature a fighter type creature and a healer or druid type creature and then sometimes a pure caster in the mix so it is incredibly challenging for the DM and the group. sometimes all those creatures are aspects of 1 creature and each aspect gets its own initiative etc etc. 

You can defiantly scale up difficulty to the point where its is a 10% chance of getting a hit etc so this is more of a you as a DM properly scaling than the group being too strong from what I can tell. 

I would make sure the content you're putting forward isn't too linear, as this might be a reason why they're burning through it so fast. If a standard session is something like "get mission at bounty board, talk to npc, fight, find trophy, done" then yeah, that's going to go quickly. Leaving quests open-ended and leaving them multiple ways they could be solved, implementing meaningful player choice, and having quests react and adapt to player choice can make for a more meaningful and less straightforward experience. 

Put something in your players way that they cant just roll out of. That's kind of vague, but its the only advice I can offer. 

SPHERE OF ANNIHILATION, SPHERE OF ANNIHILATION, SPHERE OF ANNIHILATION! CHANT THIS WITH ME!

You must always remember that while D&D is designed exclusively to be an adventure RPG by the rules, it is also, and still is, an RPG which is not something you design into a game, it's something that exists by default.  The two concepts (adventure RPG and RPG) are not mutually exclusive, but DM's tend to forget that and kind of run the game with blinders on.

The rules are like a net that is there to catch you when you are uncertain about what "should" happen next or you want there to be consequences resolved by the mechanics. 

The subtle difference here is the way you drive the story forward.  In a typical RPG, which is to say most RPG's (not adventure RPG's) the purpose of the game is not to execute rules and test the character sheets, but rather to tell a collaborative story through player and GM interaction.  There is a certain deterministic logic applied more often than the execution of rules and more typically the players, not their characters are tested.  It is the player's decisions that drive the story forward, what they say, and what they decide to do, (they being the player).  It's presumed the character is the player's avatar in such a game, but they are sort of held to account for their words and their actions with greater frequency and there are usually fewer rules applied to the GM-player interaction.

In an adventure RPG, which is to say an RPG where the testing of characters is more frequent and more common, the idea is for the experience to be more gamist.  Meaning as a player you say or do something, but we determine the outcome and often the story results based on a die roll.  You argue with the king and then you roll a persuasion check for example to determine how the king responds or you touch a trophy and make an honor check as in your example.

To offer a counter-example from another game, take Vampire The Masquerade.  Let's say a player decides to feed on and murder a person.  The consequence of that would be the player having to figure out what to do with the body.  Did they check to see if there are any CTV camera's, are there any witnesses?  These are not mechanical consequences, they are deterministic consequences based on the logic of the scene applied by the GM.  A player does not "roll" to see what happens, it's determined by the actions of the character (aka the player's decision).  The character sheet can't fix this for them but more to the point, most of the game is executed this way.

It's a subtle difference but as I said at the beginning here, D&D while designed as an adventure RPG by the rules, is not so exclusively and it's not the intention for the game to be an adventure RPG all the time.  As a DM you are sort of expected to take the reigns periodically and preferably in a way that is not predictable by the players so that what they say and what they do can't always be circumvented by the talents of their character sheets vs. the mechanics so that they need to think a little.  There needs to be some consequences of "acting without thinking".

In a game run like D&D which it is run as an adventure RPG most of the time, sometimes this can create a situation where the players stop thinking about the world in a realistic manner, they start calculating the mechanics or become reliant on the mechanics to save them and we see this even in the most story-oriented RPG groups.  For example, in Critical Role, I'm reminded of the Kiki vs. the cliff incident (https://www.youtube.com/watch?v=lfbHKyk3p2Q).  Sometimes the DM needs to remind everyone that you are in fact, not a god, the world is a real place and character sheets can't save poorly executed plans or bad decisions.

The point here is how powerful the characters are is not the end all to RPG's, it only becomes a problem if you run the game in an exclusively adventure RPG manner all the time which you really should not do, despite the fact that the game is sort of designed this way.   Apply some RPG to the adventure RPG, especially with cocky players and the situation will rectify itself.

If the problem is them rolling natural 20's all the time, then I would question how they're rolling. Is it in-person? Is it a trust system, where they roll and say "oh, I got a..." via a message? Is if visible digital rolls?

If you're playing with people who consistently roll high, then get the dice rolling out in the open. On a Virtual Tabletop this should be easy, if they are rolling in person around a real table this should also be easy. If they are rolling in a room by themselves and then telling you what they rolled over the internet, you need to move to virtual dice rolls.

The characters are made now and those good stats will be staying. I would recommend that you present them with more things which have consequence even if passed, EG fireballs "when you succeed, you take half damage). 

If the issue is that your players are finding it too easy, or that they aren't engaged, then consider what role in the story their activities are playing. Are they discovering important points about the plot, or are they killing a monster, getting the loot, and going back to town to spend it?

Mimic curse. Everything you touch turns into a mimic. Which provokes you to touch/investigate more items, spreading the curse