Neither of these solutions worked for me. If you place all your subviews into the UICollectionViewCell content view, which you probably are, you can set the shadow on the cell’s layer and the border on the contentView’s layer to achieve both results.
cell.contentView.layer.cornerRadius = 2.0f;
cell.contentView.layer.borderWidth = 1.0f;
cell.contentView.layer.borderColor = [UIColor clearColor].CGColor;
cell.contentView.layer.masksToBounds = YES;
cell.layer.shadowColor = [UIColor blackColor].CGColor;
cell.layer.shadowOffset = CGSizeMake(0, 2.0f);
cell.layer.shadowRadius = 2.0f;
cell.layer.shadowOpacity = 0.5f;
cell.layer.masksToBounds = NO;
cell.layer.shadowPath = [UIBezierPath bezierPathWithRoundedRect:cell.bounds cornerRadius:cell.contentView.layer.cornerRadius].CGPath;
Swift 3.0
self.contentView.layer.cornerRadius = 2.0
self.contentView.layer.borderWidth = 1.0
self.contentView.layer.borderColor = UIColor.clear.cgColor
self.contentView.layer.masksToBounds = true
self.layer.shadowColor = UIColor.black.cgColor
self.layer.shadowOffset = CGSize(width: 0, height: 2.0)
self.layer.shadowRadius = 2.0
self.layer.shadowOpacity = 0.5
self.layer.masksToBounds = false
self.layer.shadowPath = UIBezierPath(roundedRect: self.bounds, cornerRadius: self.contentView.layer.cornerRadius).cgPath