There were no examinations held in Fukushima this time, so I had to take the test in Sendai.
この場合さの「開催」は hold を使って下の例文のように言うと自然で良いでしょう。
ーThere were no examinations held in Fukushima this time, so I had to take the test in Sendai.
「今回は福島で試験の開催がなかったので、仙台で試験を受けなければいけなかった」
examination で「試験」
to take a test で「試験を受ける」
ご参考まで!