I have created what I believe to be a 'Vector Graphic'. If I save it as an .eps or inkscape svg, when I open it in other software it shows as a blank. I am desperately trying to create a vector graphic that can be blown up with no loss of resolution, how do I do that?

It might be the artwork you created is not within the page boundary.
 

Feel free to share an example file.

Thanks for coming back to me. See attached example file.

Your file looks fine. You could try converting the text to paths, some sw does not recognize some fonts.

Which other software don´t recognise the vector data then?

Tyler, how do I convert to paths as the only option it's giving me is convert to text!

Look under Path->Object to Path.

Tyler,

Is this any better and is it scaleble with no loss of resolution?

The first and second line of text could also be converted to paths.

The original file was fine as far as scaling is concerned. The question is still what software has a problem opening the file?