I have no experience with EMFs in particular, but the general problem when converting between different vector formats is that certain objects (such as text, Bézier polygons with borders or gradients) are not available in the target format. Ideally, Inkscape converts its objects to objects which are supported by the target format. If you experience losses during conversions, this conversion failed for some reason or Inkscape does not convert the objects as they are supported by a higher version of the target format than the one you need.
Thus, if some objects are lost in format conversion, you can sometimes work around this by manually converting them (in Inkscape) to more primitive objects before format conversion. In most cases, Object to Path will do the job. What objects you need to convert exactly and to which extent, is however something you have to find out by experiment. Also, this can be quite tedious.