In a Japanese English grammar textbook, "seems" is translated as ~のように見える, for example:
He seemed to have been ill.
病気であったように見えた。
I've also seen "seems" written as ~(の)ように思える in various example sentences on Space ALC:
何の効果もないように思える。
It doesn't seem to have an effect.
What's the difference in meaning and usage between ~(の)ようだ, ~(の)ように見える, ~(の)ように思える and ~みたい?
