I have extended the solution of Alex Klaus to prevent input of too long texts.
public class TextBoxMaxLengthBehavior : Behavior<TextBox>
{
    public static readonly DependencyProperty MaxLengthProperty =
        DependencyProperty.Register(
            nameof(MaxLength),
            typeof(int),
            typeof(TextBoxMaxLengthBehavior),
            new FrameworkPropertyMetadata(0));
    public int MaxLength
    {
        get { return (int) GetValue(MaxLengthProperty); }
        set { SetValue(MaxLengthProperty, value); }
    }
    public static readonly DependencyProperty LengthEncodingProperty =
        DependencyProperty.Register(
            nameof(LengthEncoding),
            typeof(Encoding),
            typeof(TextBoxMaxLengthBehavior),
            new FrameworkPropertyMetadata(Encoding.Default));
    public Encoding LengthEncoding
    {
        get { return (Encoding) GetValue(LengthEncodingProperty); }
        set { SetValue(LengthEncodingProperty, value); }
    }
    protected override void OnAttached()
    {
        base.OnAttached();
        AssociatedObject.PreviewTextInput += PreviewTextInputHandler;
        DataObject.AddPastingHandler(AssociatedObject, PastingHandler);
    }
    protected override void OnDetaching()
    {
        base.OnDetaching();
        AssociatedObject.PreviewTextInput -= PreviewTextInputHandler;
        DataObject.RemovePastingHandler(AssociatedObject, PastingHandler);
    }
    private void PreviewTextInputHandler(object sender, TextCompositionEventArgs e)
    {
        string text;
        if (AssociatedObject.Text.Length < AssociatedObject.CaretIndex)
            text = AssociatedObject.Text;
        else
        {
            //  Remaining text after removing selected text.
            string remainingTextAfterRemoveSelection;
            text = TreatSelectedText(out remainingTextAfterRemoveSelection)
                ? remainingTextAfterRemoveSelection.Insert(AssociatedObject.SelectionStart, e.Text)
                : AssociatedObject.Text.Insert(AssociatedObject.CaretIndex, e.Text);
        }
        e.Handled = !ValidateText(text);
    }
    private bool TreatSelectedText(out string text)
    {
        text = null;
        if (AssociatedObject.SelectionLength <= 0)
            return false;
        var length = AssociatedObject.Text.Length;
        if (AssociatedObject.SelectionStart >= length)
            return true;
        if (AssociatedObject.SelectionStart + AssociatedObject.SelectionLength >= length)
            AssociatedObject.SelectionLength = length - AssociatedObject.SelectionStart;
        text = AssociatedObject.Text.Remove(AssociatedObject.SelectionStart, AssociatedObject.SelectionLength);
        return true;
    }
    private void PastingHandler(object sender, DataObjectPastingEventArgs e)
    {
        if (e.DataObject.GetDataPresent(DataFormats.Text))
        {
            var pastedText = Convert.ToString(e.DataObject.GetData(DataFormats.Text));
            var text = ModifyTextToFit(pastedText);
            if (!ValidateText(text))
                e.CancelCommand();
            else if (text != pastedText)
                e.DataObject.SetData(DataFormats.Text, text);
        }
        else
            e.CancelCommand();
    }
    private string ModifyTextToFit(string text)
    {
        var result = text.Remove(MaxLength);
        while (!string.IsNullOrEmpty(result) && !ValidateText(result))
            result = result.Remove(result.Length - 1);
        return result;
    }
    private bool ValidateText(string text)
    {
        return LengthEncoding.GetByteCount(text) <= MaxLength;
    }
}
In the XAML I can use it like this:
<DataTemplate DataType="{x:Type vm:StringViewModel}">
    <TextBox Text="{Binding Path=Value, UpdateSourceTrigger=PropertyChanged, ValidatesOnNotifyDataErrors=True}">
        <i:Interaction.Behaviors>
            <b:TextBoxMaxLengthBehavior MaxLength="{Binding MaxLength}" LengthEncoding="{Binding LengthEncoding}" />
        </i:Interaction.Behaviors>
    </TextBox>
</DataTemplate>
where xmlns:i="http://schemas.microsoft.com/expression/2010/interactivity". I hope that this will help somebody else.