The phrase "seemed sure that" is grammatically correct and can be used in written English.
It is typically used to express someone's confidence or certainty about something. Here is an example: "She seemed sure that she would ace the exam, having studied for hours the night before."
He seemed sure that he could make money no matter who ended up in charge.
"The end is near," he said, although he seemed sure that the end of Klitschko's reign as champion was even nearer.
In recent months, as it seemed sure that the city would evict the gardeners, they fortified land they had come to see as their own.
Few people I talked with in Nicaragua seemed sure that the canal would be completed, but everyone hoped that it would help the economy: even if only a railroad or a port was built, it was better than nothing.
They'd had four children in the home and had recovered only three, but they seemed sure that their missing child wasn't among those who'd been shut in the schoolroom.
The crowd applauded both boxers at the end, although the bipartisan mood lasted only until the judges' decision was announced: one judge had Vargas slightly ahead, but the other two scored it even, which meant a draw, and more booing; Salido had been the fan favorite, and it just so happened that most fans seemed sure that he had won.
This time, politicians seemed surer that people would soon head back to the shops.
At least one Jeter fan seems sure that they will.
Penguin seems sure that the self-education urge is still strong.
Both sides seem sure that repeating their respective greatest hits (Make the rich pay their fair share!
The regime seems sure that it can keep the area under control, aided perhaps by the Americans.
