I feel fairly comfortable with awarding and penalizing honor and glory, but I'm not sure my players really care or see the affects.

What are some ways I can make those scores feel meaningful to my players? Like mechanical things I might be overlooking.

Do your players know about the advantages and disadvantages associated with high and low Honor and Glory scores? Check out page 302 for the table on when Honor mechanics kick in and 304 for the one on Glory.

If that's not enough, maybe introduce something like the Honor rolls from previous editions? Let players reroll an action if they stake an amount of honor. Or have a Mjolnir-type katana that can only be wielded by the worthy. Or give everyone Warrior's Resolve or Courtier's Resolve for free.

But I guess I'd say if the entire group doesn't seem that interested in Honor and Glory mechanics, maybe it's okay to just not worry about them too much.

Try to talk to your players about the 'issue'.

Maybe it isn't as bad as you thought, maybe it's even worse.
The important thing here is not to start pushing and pulling mechanical levers to coerce them, but instead make sure that everybody is on the same page about what you are all playing and what the numbers mean.

In short be Open, Honest and Cordial.
But must importantly talk with the group.

10 hours ago, Goken91 said:

What are some ways I can make those scores feel meaningful to my players? Like mechanical things I might be overlooking.

The Warrior's Resolve kata and the Courtier's Resolve shuji are very powerful at high honor/glory scores and available at rank 1.

As a not-too-unrealistic example, my own actual character is a rank 1 shugenja with a Yoriki title. He has Warrior's Resolve, 8 Endurance, 8 Composure, Honor 71, Glory 55.
Let's say he gets into a one-on-one fight with some opponent who deals 5 points of Fatigue damage after armor, no crits. The opponent wins initiative.

1) Fight without Warrior's Resolve: Opponents deals 5 damage, I hit him back for whatever damage, he hits me again for 5 damage. I have taken 10 damage, so I am Incapacitated with 2 excess Fatigue, my combat is lost, I probably die.

2) Fight with Warrior's Resolve: Opponents deals 5 damage, I hit him back for whatever damage, he hits me again for 5 damage. I have taken 10 damage, so I I am Incapacitated with 2 excess Fatigue. I enter Water Stance if not there already, spend 1 Void Point for Warrior's Resolve and instantly heal 7 Fatigue, bringing me to 3. Since Warrior's Resolve needs no roll, I can do it both while Incapacitated, and as my bonus action in Water Stance, meaning I can still do a regular non-support action on the same turn with a roll. So I attack and hit him for whatever damage. He hits me again for 5 points of damage, bringing my total to 8. I am still standing and not Incapacitated, so I hit him again for whatever damage.

The number of times I could attack in this hypothetical example increased by 200%, from one to three. That is a very big difference.

Something similar might play out with Glory, Courtier's Resolve and a duel, with the main difference that there I have to use it BEFORE becoming Compromized. Still, it would probably extend the time I can duel without taking a Finishing Blow by 50+%, so another important difference.

You might think that those mechanical differences are rather obscure, somewhere deep in two of dozens techniques, and I would both agree and think it is deliberate. Honor and Glory are central to L5R campaigns, but as struggling with the demands of Honor and Glory and their conflicts is one of the central themes, having a mechanism that clearly advantages e.g. maximizing Honor would undermine the play. Players should be free to do the dishonorable thing or the unglorious thing if they think that is what their character should do. Some shudder to remember Paladins on former D&D editions who lost their magic powers because their assassin partymember killed someone. Clearly, L5R didn't want to go into such a strict mechanical consequence of honorable or dishonorable actions.

(Some might argue that something like Honor should need no mechanical reward, being central to the play itself, others might disagree. But the OP asked for mechanical things, so I provided some.)