A famous company...
or a highly respected company....

Würde man das in einem förmlichen Anschreiben benutzen?

I'd sooner go with Todd's second suggestion.
A renowned company *might* work, too, but famous is a bit overdone (imo)

I am looking for the same impression in english. Isn't there any proper translation?

My own suggestions is to use the word "anerkannt" (engl. "accepted", "accredited", "acknowledged" or "well recognized").

So, basically I would recommend to use any of these words in combination with "well", or something equivalent.

"highly-respected company" (note that it's hyphenated) IS a proper translation.

reputable company