At last week's gathering at Merkaz HaRav, one of the rabbis that spoke was Rav Eitan Eisman. Rav Eisman was the director of the Chief Rabbinate when Rav Shapira zt"l was Chief Rabbi. He had a lot of great stories to tell about Rav Shapira, including the following:
Rabbi Shapira had sons that had reached the age to get married, and he was trying to find them suitable brides. He asked a somebody if he knew of anyone suitable, and the person asked the Rav exactly what kind of girl is he talking about. The Rav responded that the girl must have middot tovot, good character traits. The person than inquired if the Rav also required that the girl have yichus, a prestigious family line. Rav Shapira replied using his great humor saying,"You bring the girl with good middot, and I'll bring the yichus!"