Across the Plaza de la Armeria from the Royal Palace is the Catedral de Santa Maria la Real de la Almudena.
The foundation stone was laid in 1883, and completed in 1993 with consecration by St. John Paul II.
Wiki tells us that "On 22 May 2004, the marriage of King Felipe VI, then crown prince, to Letizia Ortiz Rocasolano took place at the cathedral."
I didn't go inside, but I understand that the interior is neo-gothic.
Close-ups on the panels on both ends are seen in the next set of photos.