According to Lowagie:
PdfPCell cell = new PdfPCell(new Phrase("blah Blah blah");
cell.setVerticalAlignment(Element.ALIGN_MIDDLE);
This is always correct in a technical sense, but sometimes looks bad.
To center, draw a box around the object, find its middle, and align it with the center of its surrounding object.
iText thus finds the center of the phrase, and aligns it. But human eyes sometimes focus on the bulk of text, say the parts of the font between the baseline and the cap height. So to have it look good, you need to center relative to that.
Phrase content = new Phrase("Blah blah blah", Font);
Float fontSize = content.getFont().getSize();
Float capHeight = content.getFont().getBaseFont().getFontDescriptor(BaseFont.CAPHEIGHT, fontSize);
Float padding = 5f;
PdfPCell cell = new PdfPCell(content);
cell.setPadding(padding);
cell.setPaddingTop(capHeight - fontSize + padding);
Note that the PdfPCell method setVerticalAlignment(..) isn't used.
It seems like this wouldn't necessarily work for a multi-line phrase, but it does.

The problem would be obvious if iText could show bounding boxes around things (mind, you can tell iText to draw bounding boxes, it's just more work than a magical on/off switch).
This solution is adapted from an email from Paulo Soares.