You need to start by overriding the DataGridViewCell.PositionEditingPanel Method. You need to redefine your own type of column and your own type of cell to access this method.

Here is an example on how to do it, that multiply the size of the editing panel (the one that owns the editing control) by 2:

dataGridView1.AutoGenerateColumns = false; // disable columns auto generation

... add all columns

// add your special column
col = new MyColumn();
col.DataPropertyName = "Text"; // bind with the corresponding property
dataGridView1.Columns.Add(col); // add the custom column

... add other columns

public class MyCell : DataGridViewTextBoxCell
{
    public override Rectangle PositionEditingPanel(Rectangle cellBounds, Rectangle cellClip, DataGridViewCellStyle cellStyle, bool singleVerticalBorderAdded, bool singleHorizontalBorderAdded, bool isFirstDisplayedColumn, bool isFirstDisplayedRow)
    {
        cellBounds.Width *= 2;
        cellClip.Width = cellBounds.Width;
        return base.PositionEditingPanel(cellBounds, cellClip, cellStyle, singleVerticalBorderAdded, singleHorizontalBorderAdded, isFirstDisplayedColumn, isFirstDisplayedRow);
    }
}

public class MyColumn : DataGridViewTextBoxColumn
{
    public MyColumn()
    {
        CellTemplate = new MyCell();
    }
}