The quickest would be to instantiate your Guid outside of your methods and re-use it. I suggest some more reading on the basics though. Since your update includes mention of a different clients you need to provide more detail of the system. Maybe you could pass the Guid around through the server? Hard to say without some detail.
Guid myGuidToReuse = Guid.NewGuid();
public void method1()
{
using (new Tracer(myGuidToReuse.ToString()))
{
}
}
public void method2()
{
using (new Tracer(myGuidToReuse.ToString()))
{
}
}