In general opinion or estimation. In later use applied to titles given by courtesy. Obsolete.

at a premium: above the usual or nominal price, above par; (of a service or commodity) worth more than usual, esp. because scarce and in demand…

After to. With preceding quantifier or adverb of degree. much (also greatly, little,etc.) to the credit of: so as to reflect very well, not very…

Up on a level with (something else highly rated). colloquial.