We have found 3 software records in our database eligible for .vsd to .vsdx file format conversion.
It should be possible to just simply re-save (File ► Save as..) VSD files to VSDX format in the latest version of Microsoft Visio.
This seems to be the most convenient and perhaps also only reliable way how to achieve this conversion. However, LibreOffice apparently also supports at least some versions of Visio formats.
Updated: August 19, 2016
A diagram application, that uses vector graphics to create diagrams. Microsoft Visio is distributed as part of Microsoft Office Family and also available as a subscription through Microsoft Office 365. The latest version is Visio 2016 that is compatible with Windows 7, Windows 8 and Windows 10.