The Ukrainian official companies register can be found at http://irc.gov.ua/ua/Poshuk-v-YeDR.html. The interface and information is in Ukrainian only but Google’s translation option does a good enough job to help you through the site. If you use Google Chrome as your browser you can enable its automatic translation prompt by going to Options, Under the Bonnet, and ticking the Translate box. Many thanks to Ladymyr Bondar for alerting me to the site.