If you're looking for manga similar to Cerulean no Sora no Kanata ni: Kuro Hakushaku ni Aisarete (Light Novel), you might like these titles.
Up until now, the most exciting part of Minori's schoolgirl life has been playing video games... but one day, her skills win more than she ever could have imagined. When Minori beats some guy at the local arcade, suddenly he declares he's going to marry her! When the same guy turns out to be none other than Kanata Okazaki – Japan's newest, youngest-ever prime minister – Minori finds herself swept up in a world of politics and paparazzi. Is Kanata really in love with her? Exactly why does his 18-year-old senior aide glare at Minori all the time? How is it Japan can be run by such a young prime minister, anyway?!
This woman is too strong to be protected. Ichika Kiryuin is the only daughter of a large corporation. Hayama Shuzuku was born into a family, the Samurai, that worked as bodyguards for generations, and was taught to live only as a disposable shield. Hayama was ready to guard and protect Ichika, but it turns out Ichika, who has a strong physique, will be protecting him?!