While I appreciated the invite I received to the fancy ball, I had other plans that night and had no choice but to offer a declination in response.

Since it is rude to not respond to an invite, you should always give some sort of formal declination if you are invited to something you cannot attend.

The two ambassadors were trying to reach an agreement so their countries could work together, but they both offered a declination to the treaty that had unfavorable terms.

We offered our enemies the chance to surrender honorably, but the only thing they offered in return was declination and a declaration that they would fight to the death.

The formal invite to the party was met with an equally formal declination on my part, since I had no desire to attend.