Which phones or Dual band or Quad Band?

When I visited my son in Japan in last December, my phone would not work at all except with Wifi. My carrier told me that it would work if I swapped sim cards, but it turned out that I needed Dual Band or Quad Band to connect at all in Japan.

Which phones or Dual band or Quad Band, and which will work in Japan? When I look at phones specs, it often does not say one way or the other.

Which phones are Quad Ban