Trustworthy, a.
Worthy of trust or confidence; trusty. -- Trust"wor`thi*ness, n.
Shades of meaning
Fernald has no entry of its own for trustworthy; he lists it under authentic, faithful, honest, reliable.
Where he writes about it:
We speak of accepted conclusions, certain evidence, current money, genuine letters, a legitimate conclusion or legitimate authority, original manuscripts, real value, received interpretation, sure proof, a true statement, a trustworthy witness, a veritable discovery. — from authentic
Trusty and trustworthy refer to inherent qualities of a high order, trustworthy being especially applied to persons, and denoting moral integrity and truthfulness; we speak of a trusty sword, a trusty servant; we say the man is thoroughly trustworthy. — from reliable
A man is said to be reliable with reference not only to moral qualities, but to judgment, knowledge, skill, habit, or perhaps pecuniary ability; a thoroughly trustworthy person might not be reliable as a witness on account of unconscious sympathy, or as a security by reason of insufficient means. — from reliable
A reliable messenger is one who may be depended on to do his errand correctly and promptly; a trusty or trustworthy messenger is one who may be admitted to knowledge of the views and purposes of those who employ him, and who will be faithful beyond the mere letter of his commission. — from reliable