Hi Rohit, Thanks a lot for your answer. With Mathematica 11.2 using:the code

ClearAll[check, val, max]
check[n_] := n <= max
val = 5;
max = 10;
{InputField[Dynamic[val, (If[check[#], val = #, max] &)], Number], 
Dynamic[val]}

when I first first enter for instance 4 in the inputfield I get 4 as a result. That is as it should. But when I then enter 11, which is higher than the allowed maximum 10, I get again 4. I had prefered getting 10. But I can live with it.

The code that you suggested for the button case works perfectly.

I combined things in the following code for a CDF: Here the maximum is variable. It depends on the date.

Export["Preventing that input in an InputField exceeds a certain \
value.cdf",
 CreateDocument[ {TextCell[
    "Preventing that input in an InputField exceeds the value of max"],
   DynamicModule[{val, max, check},
    Column[{
      check[n_] := n <= max;
      max = QuantityMagnitude[DateObject[] - DateObject[{2021, 1, 1}]];
      val = max;
      Row[{  
        InputField[Dynamic[val, (If[check[#], val = #, max] &)], 
         Number], Dynamic[Button["-", val--]], 
        Button["+", If[check[val + 1], val++, max]]   }],
      Row[{Dynamic[val]}]    }]]  }]]

This works nicely, but still with not the possiblity of getting the maximally allowed value as a result if a too high value is entered in the input field. You might still have a suggestion for getting this? Then I would be still more happy than I am now.

Hi Laurens,

You could experiment with something like this

ClearAll[check, val]
check[n_] := Between[n, {5, 10}]

val = 6;
{InputField[Dynamic[val, (If[check[#], val = #, val] &)], Number], Dynamic[val]}

If the input value is between 5 and 10 it will be accepted, if not the old value is retained. This works in a notebook, I have not tested it in a CDF.