In the example below, the prepreg (composite fibers "pre-impregnated" with an epoxy) can be added or removed in 1 mil increments to affect H, and changes can also be made to W or W1. Multiple iterations may be needed depending on the design.
At higher frequencies, the impedance will depend on the geometry of the circuit so it has to be calculated. These calculations are complex. Below is an example from polar SI9000.
In the case of a microstrip, the impedance will depend on 4 parameters:
1.H is the height of the dielectric. It can be changed in steps. In this example +/- 1 mil results in +/- 2 ohms.
2.Er is the dielectric of the material. It is fixed once the material is chosen. Having a good idea of the Er is necessary since +/- 0.1 results in +/- 0.5 Ohms. To make things more complicated, only certain specialty materials like Rogers 4003 have well-defined dielectrics.
3.T is the trace thickness. An outer trace is plated, providing a 20% uncertainty in exterior traces. This results in a small uncertainty of +/-0.2 ohms.
4.W is the top trace width. Typical trace width uncertainty is +/-2 mil which results in an uncertainty of +/- 2 ohms.
5. W1 is the bottom trace width. Typical trace width uncertainty is +/-2 mil which results in an uncertainty of +/- 2 ohms.
In the example provided, if the target impedance is 50 ohm, a 26 mil trace width is required. Since there is a tolerance on the input parameters it translates into a tolerance on the trace width. Achieving the calculated trace size should result in the required impedance.
A typical tolerance on final impedance is +/-5% for less than 50 ohm impedance line, +/-10% for less than 100 ohm impedance line in SysPCB Shenzhen China.
Ensure your PCB manufacturer has the knowledge and capabilities to meet your requirements, like you want to ensure the line width firstly or impedance. Also ask them to send engineering question regarding this, now that every PCB manufacturer owns this kind of software, it is not a high tech to simulate the value, but to ensure the actual impedance in pcb process is really not a easy job to do.