It is absolutely necessary to be in possession of official calibration certificates issued by accredited laboratories for appliances that must be calibrated?

Only a few standards demand calibration by accredited laboratories. On the other hand, the requirement for metrological traceability is included in numerous reference standards, such as ISO/IEC 17025, ISO 15189, ISO 9001 paragraph 7.6, etc. The accrediting agency in each country specifies the particular requirements for traceability for organisations applying for accreditation, on the basis of the ILAC P 10 document.