In accordance with what is appropriate or suitable for the circumstances:
— I met the junior senator from Illinois and I was duly impressed.

synonyms: appropriately, befittingly, fitly, fittingly, properly, suitably.

Roget 924: duly, ex officio, de jure [Lat.]; by right, by divine right; jure divino [Lat.], Dei gratia [Lat.], in the name of.