Common words that rhyme with significant include insignificant, cant, scant, penchant, brilliant, indignant, unimportant, pleasant, slant, unpleasant, valiant, radiant, fulgurant, vibrant and buoyant.
His comment seemed insignificant in the grand scheme.
Her abdication left the throne vacant.
The smell triggered instant disgust.
The court issued a warrant for his absconding.
Everyone praised her brilliant performance.
His opinion seemed completely unimportant to them.