Within the LokiCheckout, we simply make use of the Magento core capabiliteit to validate VAT numbers. And it is made visually appealing if validation errors occur.
Whenever a customer enters a VAT number, the LokiCheckout is able to validate this number properly. First of all, a field prefix is populated with the current country value that the customer supplied (including a remapping when the VAT country is not equal to the Magento country ID, like with GR and EL). Next, the customer is able to enter a VAT ID that starts with that prefix. If the VAT number does not validate, it is not added to the quote.
The EU VAT Enhanced module of Geissweb is a popular solution to validate EU VAT numbers. While this third party module is not required for the validation of modules itself, it is handy to have anyway.
See Yireo_LokiCheckoutGeisswebEuvat