All orchestras worthy of the name have personalities, and no two are alike. Compared with some American orchestras — the 177-year-old New York Philharmonic, for instance — the National Philharmonic is still a relative toddler. But it most definitely has a distinctive personality, as I am pleasantly reminded once or twice a season, when I hear them at Strathmore.

The strings are rich, lustrous and, best of all, they can move. The wind choirs are pungent and full of character. Those French horns, whether playing as a duo, quartet or octet, are simply a joy to hear. Piotr Gajewski, the orchestra’s ­Polish-born music director, has good ideas and the technique to achieve them. Instead of a baton, he uses the most economical hand gestures to communicate with his musicians. The vibe in the audience is that everybody onstage is happy, and maybe a little proud to be there, and the music sounds that way.

Saturday night’s program re-created a 1943 Carnegie Hall concert in which a 25-year-old Leonard Bernstein, with virtually no notice, stepped in to conduct for the ailing Bruno Walter. The concert was broadcast on radio nationally and proved to be the career launch of one of America’s most gifted composer-conductors. Gajewski, incidentally, studied with Bernstein at Tanglewood.

Schumann’s moody overture to his incidental music for Byron’s “Manfred” was the opener. From there on, it was one orchestral showpiece after another, each beautifully wrought. The Theme, Variation, and Finale, Op. 13 was the first great success of the Hungarian American Miklós Rózsa, certainly opening doors to his storied career in Hollywood. The orchestra handled its heady blend of lush 1930s sound and Hungarian folk sources persuasively. Heavier lifting awaited in Strauss’s “Don Quixote,” where solo cellist Zuill Bailey and violist Roberto Díaz added their superb playing to a touchingly human reading of this challenging work. Finally, the prelude to Wagner’s “Die Meistersinger,” in an ample, forthright and earnest performance, seemed both a summation and a valediction.