IPA: /ˈdjuːkəli/
KK: /ˈduːkəli/
In a way that is suitable for a duke or reflects the dignity of a duke's rank.
The banquet was held ducally, with grand decorations and elegant attire.
Ducally → It is formed from "duc-" (from Latin "ducere", meaning to lead) and "-ally" (a suffix meaning in a manner relating to). The word "ducally" means in a manner relating to leading or leadership.
Think of 'leading' ('ducere') to remember that 'ducally' refers to something done in a manner related to leadership.