If your screen resolution is the same as your client's, and you are both using monitors with the same standard aspect ratio (typically, today, 16:9 for desktop monitors) ... the client should have no problem.
Welcome to the great puzzle of dealing with different display device sizes, screen resolutions, and aspect ratios: [
^].
An example of how it gets complex: the screen resolution I use ... because of vision problems I need to see things BIG ... is 1360/768 (ratio 683:384) which does not map exactly to 16:9 or 16:10 ... or 4:3. The reasons for this resolution becoming frequently used some years ago involved manufacturing efficiency, computational efficiency, 8-bit screen memory device limitations, and consumer demand for wider screens than 1024/768 provided.
I suggest you consider it part of your application design to research the possible future use of your application on devices with different form-factors and screen-display characteristics.
In dealing with the client, I suggest you make it part of your contractual agreement that you specify the different monitor screen ratios the UI is designed for, and whether the app can be used if the monitor is in "portrait" rather than "landscape" orientation.
If you use WPF, you have the benefit of a completely vector-based graphic engine ... however, that does not guarantee your app will look "perfect" at any arbitrary size ! Windows Forms's GDI+ graphics engine is much more limited.
In any case, fonts in smaller sizes than #14 are always going to look best at certain
discrete sizes; that's because they are "hinted" so that pixel adjustments are made to optimize screen readability. Trying to scale Fonts is not a good idea. So, for fonts at small sizes, you need to identify those discrete sizes and "jump" between them, rather than scale.
Observe what happens when, in a WinForms project, you select a Form and set its 'Font property to Consolas #10 ... in the Designer.cs file, you'll see this:
this.Font = new System.Drawing.Font("Consolas", 10.2F, System.Drawing.FontStyle.Regular, System.Drawing.GraphicsUnit.Point, ((byte)(0)));
If you had chosen Consolas #9, the value would be #9; that value of #10.2 is the result of Windows looking up the optimum size at which hinting will be most effective.
I'd at least
consider trying to make effective UI appearance at 1024x768, 1360x768, and 1920x1080.
And, certainly, study and try the other ideas in the solutions/comments offered to you here by OriginalGriff and Phillippe Mori !
I suggest you get familiar with these different Areas/Bounds properties of the WinForm app and Form:
private Rectangle
screenBounds,
screenWorkingArea,
formDesktopBounds,
formBounds,
formClient,
formDisplay;
private GetScreenFormInfo()
{
var priScreen = Screen.PrimaryScreen;
screenBounds = priScreen.Bounds;
screenWorkingArea = priScreen.WorkingArea;
formBounds = Bounds;
formDesktopBounds = DesktopBounds;
formClient = ClientRectangle;
formDisplay = DisplayRectangle;
}