A romantic partner who would willingly agree to have a Pokémon-themed wedding means that they are a real catch, and what better way to catch them than by tying the knot in a ceremony attended by two people in giant Pikachu mascot costumes.
There is a company in Japan called ESCRIT that specializes in wedding ceremonies. ESCRIT now offers official Pokémon-themed weddings for any couple who wishes to have their wedding cake and decorations adorned with Pikachu. The official Pokémon website features images of one such ceremony taking place (thanks, Kotaku).
The Pokémon-obsessed bride and groom can have a ceremony that is attended by people in Pikachu costumes, both of which are dressed as if they are also getting married. The decorations feature images of a male and female Pikachu staring lovingly into each other's eyes, while the wedding certificate features a beautiful piece of artwork of the same love-ridden Pikachu. The tables feature Pokémon plushies (such as the Eeveelutions), while the food is also shaped like Pokémon and Pokémon-related items. The wedding cake is adorned with fruit and sweets that bear images of Poké Balls.
There is currently no word whether the bride and groom can select other Pokémon to be featured in their wedding. There might be a couple of Magikarp fans in Japan who were lucky enough to find each other and their wedding day will only be complete if two people in Magikarp costumes are flopping around while the vows are shared. It's up to ESCRIT to deal with them (if they exist).
Themed weddings have been around for a long time, yet video game weddings are a modern occurrence. It's possible for fans of Final Fantasy XIV to have a wedding ceremony that matches the one from the game, while Minecraft-themed weddings allow the bride and groom to make cheap, block-shaped decorations for the event.
There is nothing stopping a bride and groom from holding an unofficial Pokémon wedding, as Game Freak isn't likely to stop the ceremony with a lawsuit, but the romantic Pokémon fans in Japan can at least be married in a way that is officially endorsed by Pikachu.