Graciously

adv.kind, calmwarm

What it means

With warm courtesy, generosity, and respect for another person's dignity.

Reach for it when describing a socially considerate response, especially when status or disappointment could create tension

The host graciously found seats for the late arrivals.

playful
with good grace
someone accepts inconvenience without resentment
not when The phrase fits acceptance better than active hospitality or generosity.
everyday
generously
credit, time, or resources are freely shared
not when Generously emphasizes amount and not the tact of the manner.
everyday
politely
basic social respect is all the evidence supports
not when Politeness can be minimal and lacks gracious warmth.
warm
kindly
benevolent intent is more important than polished manners
not when Kindly can sound patronizing in an instruction or command.
formal
courteously
recognized standards of respectful behavior are being followed
not when Courteously may be correct but emotionally cool.
literary
magnanimously
a winner or injured party rises above resentment
not when Magnanimously is grand and can make ordinary civility sound heroic.

graciously accept
The runner graciously accepted second place and praised the winner's finish.
graciously offered
The museum graciously offered a quiet room for the community meeting.
graciously declined
She graciously declined the honor so the whole team could be recognized.

The definition and the example on this page are written here. The dictionaries above ground which meaning is being described, not the wording.