Concertos remained popular during the Romantic period (roughly the 19th century). There were many written for piano and violin.
The Romantic concerto:
Beethoven wrote five piano concertos and a violin concerto. The violin concerto flourished and some of the most well-known pieces were written during this period. The composers Mendelssohn, Tchaikovsky and Brahms wrote violin concertos at this time.
In the last movement of Mendelssohn’s Violin Concerto in E minor there is a showy passage. This piece highlights the interplay between violin and orchestra.