As you wind up planning and planting your blue flowered garden, top it off with a generous flourish of blue flowers on a blue flowered vine.
The annual morning glory "Heavenly Blue" with its amazingly huge brilliant blue blooms is a natural choice. If you use this, remember that morning glories close their flowers in the afternoon and evening and on cloudy days.
Asarina scandens "Sky Blue" is a smaller and more delicate annual vine, with gloxinia-like trumpet shaped blooms. Grow this in a hanging basket if you like, so you can enjoy the blue flowers up close.
Or, you could plant Clematis if you prefer a perennial vine. "Will Goodwin" for example is a popular variety with true blue coloring. There are so many new and different (and gorgeous) clematis available today with more cultivars coming on the market all the time. This is another plant worth seeing in bloom before making a decision as to the "best" shade of blue flower for your garden.
Vines tend to be luxuriant growers. They can be used to purposely cast shade if grown on a trellis or tuteur in the open garden, or they can be used to soften the look of a fence or wall. Smaller vines can be grown in containers to bring them where they can be enjoyed up close.
When you consider planting a vine, take into account its mature size so you have an appropriate support to accommodate it when it is fully grown. If you plant a large vine without thinking ahead, you may find your vine growing on top of and smothering or strangling neighboring plants.