To describe a lack of bias:
* Objectively, the evidence points to a guilty verdict.
* It's difficult to objectively assess the situation when you're personally involved.
* The journalist strived to report the news objectively, avoiding personal opinions.
To describe something based on facts:
* Objectively, the company's performance has improved significantly in recent years.
* The data shows, objectively, that this is the most effective solution.
* Objectively speaking, the new design is more functional than the old one.
To contrast with subjective opinions:
* While many people find the movie uplifting, objectively it has some plot holes.
* Objectively, the food is good, but it's not something I would personally order.
* I understand your feelings, but objectively, there's no reason to be upset.
Remember that "objectively" implies a lack of personal bias or emotional influence.