moment().tz(String);

The moment#tz mutator will change the time zone and update the offset.

moment("2013-11-18").tz("America/Toronto").format('Z'); // -05:00
moment("2013-11-18").tz("Europe/Berlin").format('Z');   // +01:00

This information is used consistently in other operations, like calculating the start of the day.

var m = moment.tz("2013-11-18 11:55", "America/Toronto");
m.format();                     // 2013-11-18T11:55:00-05:00
m.startOf("day").format();      // 2013-11-18T00:00:00-05:00
m.tz("Europe/Berlin").format(); // 2013-11-18T06:00:00+01:00
m.startOf("day").format();      // 2013-11-18T00:00:00+01:00