Warily is an adverb meaning cautiously or carefully. In order to find synonyms for this word, we need to find other words that convey a similar meaning. Some possible synonyms for "more warily" include "more cautiously," "more vigilantly," "more prudently," "more circumspectly," "more judiciously," "more suspiciously," "more attentively," "more alertly," "more apprehensively," "more carefully," and "more watchfully." Each of these words conveys a sense of caution and attention to detail, which is similar to what the word "warily" implies. Choosing the right synonym depends on the context of the sentence and the desired level of caution or care that needs to be conveyed.