A high quality nut file. A string seated in a properly filed nut will have the correct height and will also prevent extraneous string noise from the nut.
0.013" / 0,33 mm width.
A typical set for classical guitar would contain the following files:
0.028", 0.032", 0.036", 0.042"
A typical set for electric and acoustic guitars will depend on the string gauges. Always check the package for the string gauges and use the same file gauge accordingly.
A great aid in filing nuts is the H-GB4 Hosco GrooBar. This will prevent you from filing the string slot too deep.
