'trustworthily' originates from Modern English, specifically formed from the adjective 'trustworthy' plus the adverbial suffix '-ly', where 'trustworthy' itself is built from 'trust' + 'worthy' and '-ly' meant 'in the manner of'.

'trustworthy' changed from Middle English uses combining 'trust' (from Old English/Old Norse roots like Old English 'trēow' / Old Norse 'traust') and 'worthy' (Old English 'weorþ(e)') and later took the adverbial suffix from Old English '-līċ' to become 'trustworthily' in modern English.

Initially, the component words meant 'confidence/faith' (for 'trust') and 'having value' (for 'worthy'); over time the combined form came to mean 'deserving of trust', and the adverbial form evolved to mean 'in a manner deserving of trust' or 'dependably'.