There are a few correct answers, such as:
Estonia’s first win.

The first win from an ex-soviet country.

And more.

Both songs won the contest on 31 points.

All entrants have met King Charles of the United Kingdom.

All artists have attempted to return to the contest via a national final unsuccessfully.

All entries have the same conductor, Noel Kelehan.

All songs were written/co-written by Alex Papaconstantinou.

These are singer-songwriters (they wrote and performed their entry)

The entrant of the host country was born in the city where the contest was held.

All of these entries finished last in that year.

All performers were born on the 10th day of the month.

All performers were later hosts of Eurovision Song Contests.

The position they performed in the running order, was the position they finished on the leaderboard.