Emma,

Then, all fine. We are e-mailing with an European client.

Cheers

In Canada and the US we would usually say "I'll get back to you shortly".

"I'll come back to you shortly" may be a British expression.

Richard and Peachey,

I would use "get back" in this case, too (though I studied in UK for a while.)

My understanding of "come back" is more like "to physically move back to somewhere" so I don't think it fits in this case.

My colleague said, this is widely used in S.E. Asia and nobody thinks it strange...

Anyway, thanks Hermione, Richard and Peachey.