While there are thousands of great icon sets out there, such as Font Awesome, sometimes you just can't find an icon that you need. In my case, I needed an icon containing the client's logo.
After a fair amount of research, I came up with a process that seems to work fine. I'm documenting it here for my own reference really, but if you find it helpful then let me know.
First up I installed Inkscape which is a free vector editing package for Windows & Mac.
Then I went to https://icomoon.io and click on a random icon - selecting to preview it at 96x96 pixels. I clicked the "Generate SVG/PNG" from the footer menu to download it to my PC.
I opened this .svg file in Inkscape. The purpose of this exercise was just to get a correctly sized template. I then deleted the random icon and used its canvas space to create my own icon.
When I was finished I clicked on Path > Object to Path from the Inkscape menu before then saving it as a .svg file.
I then dragged this .svg file from my PC on to the http://fontello.com/ web site and, assuming it looks right, I clicked the download webfont button which gives you all the files and sample code for using your custom-made icon on a web page.