Formal:
* The manager was remiss in not informing the employees of the new policy. (Meaning: The manager failed to do something that was their responsibility.)
* It would be remiss of me not to mention the contributions of the entire team. (Meaning: It would be a mistake to not acknowledge something important.)
Informal:
* I feel remiss for forgetting your birthday. (Meaning: I feel bad for forgetting something important.)
* We were remiss in not checking the weather forecast before our hike. (Meaning: We made a mistake by not preparing adequately.)
In a negative context:
* The company was remiss in its handling of the safety issue. (Meaning: The company made a serious mistake.)
* It would be remiss of us to ignore the environmental impact of our actions. (Meaning: It would be wrong to overlook something important.)
Remember: "Remiss" is usually used in a negative context, implying a failure to do something that was expected or required.