On the international scene, Caniglia appeared in venues such as the Palais Garnier, Covent Garden, and the Teatro Colón.
She also participated in the creation of many contemporary works: Manuela in Montemezzi's La notte di Zoraima, Milan, 1931, Rosanna in Alfano's Cyrano di Bergerac, Rome, 1936, and the title role of Respighi's Lucrezia, Rome, 1937.
Caniglia regularly worked with the greatest conductors and singers, and left recordings of some of her great roles, notably Un ballo in maschera, and Aida (conducted by Tullio Serafin), Andrea Chénier and Tosca (conducted by Oliviero De Fabritiis), all opposite tenor Beniamino Gigli; La forza del destino (cond.
Gino Marinuzzi), Don Carlo, Fedora and Zandonai's Francesca da Rimini, this last conducted by Antonio Guarnieri.
Caniglia was married in 1939 to Italian composer Pino Donati (1907–1975), who was also music director of the Verona Arena, the Teatro Comunale di Bologna, and the Chicago Lyric Opera.