Refreshable Braille displays have already been developed in the past, but they remain quite bulky and expensive. Small displays contain only a single or a few Braille cells, with pins pushing into the fingertips. However, they are not as successful as larger displays because the skin is more sensitive to lateral movement than to orthogonal pressure. This, paper presents the design of linear electromagnetic actuators, which allows a considerable reduction in size and cost for such refreshable Braille displays. Different actuator concepts are compared. A new actuator is proposed and optimised by means of finite element simulations, which are verified with measurements on a prototype.