You no longer need a vaccination- or corona certificate to travel within Europe. On nederlandwereldwijd.nl you can see whether there are corona rules in other countries. Sometimes you still need to show an overview of your vaccinations, a negative test result or proof that you have recovered from corona.
Overview of vaccinations
You can find an overview of your vaccinations on mijn.rivm.nl if you have given permission to register your corona vaccinations. This is not official proof, but usually enough to travel.
You can also request a vaccination overview from the healthcare provider who administered the vaccinations. For example, the GGD or the general practitioner.