Frequency control is considered to be an important function of multi-terminal HVDC (MTDC) systems. Sharing frequency containment reserves (FCRs) among interconnected AC systems using flexible HVDC technology is particularly attractive in the European context. However, coordination of the contribution between systems with different sizes, quality requirements and dynamic characteristics requires harmonized rules and well-defined control strategies. If the controllers are not properly designed, they can lead to disproportional supports, noncompliance with the existing regulation framework, or even degradation of the frequency quality. This paper analyzes several frequency control solutions for MTDC systems in terms of the adequacy of the expected contribution to the frequency containment process. The performance analyses are then confirmed using load-frequency models coupled with a three-terminal DC system. It is revealed that certain control solutions result in insufficient performance with respect to the desired FCR provision. The proposed distributed solution for each pair of converters can be the most compliant with the existing framework while keeping the highest degrees of freedom.