I usually do it like this:

try {
  // Use the resource.
} catch( Exception ex ) {
  // Problem with the resource.
} finally {
  // Put away the resource.
  closeQuietly( resource );
}

Elsewhere:

protected void closeQuietly( Resource resource ) {
  try {
    if (resource != null) {
      resource.close();
    }
  } catch( Exception ex ) {
    log( "Exception during Resource.close()", ex );
  }
}