The path to holiness proceeds through stages. Christian meditation should rightfully begin in the first stage (called the Purgative Stage, or Stage of the Beginner) of this journey. What is formed in the soul by virtue of Christian (discursive) meditation establishes a crucial part of the foundation upon which and from which can emerge in the second stage, infused contemplation. The prayer of quiet (mentioned by JimR above) is a "substage" of the broader and general category of (infused) contemplation which is to be found in the second stage - a stage which is called the Illuminative Stage (or Stage of the Proficient) - it is here that the supernatural is experienced - and if given, is "infused", certainly not earned or developed by any natural works of the pilgrim.
I'm trying to say that the terms "meditation" and "contemplation" are mangled and abused beyond usefulness, and when used as they typically are, only confuse an understanding that is good to possess, in the journey of prayer. We can do meditation. God alone can give infused contemplation.
Forgive me please for dropping all these terms upon you, if they are new to you, but there is much misunderstanding of exactly how the interior life grows and matures. Labels and terms can sound and can be cold, academic, and far from the delicate and mystical Spirit who is at work within, in holy Love. Maturation in prayer IS maturation in divine Love and is most beautiful, an embrace of God within the soul. It ought - and deserves - to be sought with one's whole heart. And the seeking can be greatly aided by learning from the saints, and from the God-appointed witnesses and teachers of the journey.