Use async/await on synchronous operations (mainly to stay on UI thread)

I'm trying to run some stuff asynchronous. Here's my code:

    private async void SearchButton_Click(object sender, EventArgs e)
    {
         await Search();
    }

    // Inside search there is no async operation
    public Task Search()
    {
        // search for data in DB
        // update DataGridView and other elements on UI

        // How to return null/void/nothing?
        return ???;
    }

Is it illegal/bad practice to await on synchronous methods like Search()? I know I can use Task.Run(Search) instead but then Search() will be executed on another thread (not on UI thread) and I have to use Invoke() inside Search() very often.

I changed the return value of Search() method from 'void' to 'Task' so its awaitable but what do I have to return?