In a manner that is worthy of respect, admiration, or high regard; in an estimable way.
From estimable + -ly (adverb-forming suffix). The root remains Latin 'aestimare' (to value), with the adverbial suffix -ly added to transform the adjective into an adverb describing how an action is performed.
English speakers added '-ly' to almost any adjective to create adverbs—it's such a common pattern that we barely notice it, but it's one reason English has so many adverbs compared to languages like Mandarin Chinese.
Complete word intelligence in one call. Free tier — 50 lookups/day.