Another solution, without using any "unsecure" string in the middle, is to adapt the Window code, something like this:

Let's suppose I have an MVVM object like this, with WPF validation using IDataErrorInfo:

public class MyObject : INotifyPropertyChanged, IDataErrorInfo
{
    ...
    public SecureString SecurePassword
    {
        get
        { ... }
        set
        {
            ...
            OnPropertyChanged("SecurePassword");
        }
    }

    ...

    string IDataErrorInfo.Error { get { return Validate(null); } }
    string IDataErrorInfo.this[string columnName] { get { return Validate(columnName); } }

    private string Validate(string memberName)
    {
        string error = null;
        ...
        if (memberName == "SecurePassword" || memberName == null)
        {
            // this is where I code my custom business rule
            if (SecurePassword == null || SecurePassword.Length == 0)
            {
                error = "Password must be specified.";
            }
        }
        ...
        return error;
    }

}

And a Window Xaml with a PasswordBox like this:

<PasswordBox Name="MyPassword" PasswordChanged="MyPassword_Changed" ... />

Then, the corresponding Window code like this will trigger PasswordBox binding:

// add a custom DependencyProperty
public static readonly DependencyProperty SecurePasswordProperty =
    DependencyProperty.RegisterAttached("SecurePassword", typeof(SecureString), typeof(MyWindow));

public MyWindow()
{
    InitializeComponent();

    DataContext = myObject; // created somewhere

    // create a binding by code
    Binding passwordBinding = new Binding(SecurePasswordProperty.Name);
    passwordBinding.Source = myObject;
    passwordBinding.ValidatesOnDataErrors = true;
    // you can configure other binding stuff here
    MyPassword.SetBinding(SecurePasswordProperty, passwordBinding);
}

private void MyPassword_Changed(object sender, RoutedEventArgs e)
{
    // this should trigger binding and therefore validation
    ((MyObject)DataContext).SecurePassword = MyPassword.SecurePassword;
}