One of the pious customs of my pre-Vatican II Catholic boyhood was "making a visit to the Blessed Sacrament".  The priests and nuns would encourage us to enter the church when Mass was not being said, kneel at the communion rail in front of the high altar, and pray while focusing our attention on the tabernacle (only Anglicans called it an "aumbry") where the reserved consecrated bread--no wine in those days--was kept.  Since Christ was "truly present" in the sacrament of the Eucharist, we could feel that we were in the presence of God Himself. 

This devotion also exists among high-church Anglicans, as seen in the excerpt below of a brief essay by Fr William, a member of St Gregory's Abbey in Three Rivers, MI.  Note his emphasis on the notion that silence and stillness "work" just as well as verbal prayer in this situation.

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...I don't know why I find it easy to recreate and extend that liturgical silence when I make a visit to the reserved Sacrament.  But I do.  For me it's one of those times when the best response to God's self-manifestation is an awe-filled and deep quiet...

Certainlty words are important...For love to have meaning and to survive, the lovers have to talk to each other, and listen to each other.

But in addition to the exchange of words and the mutual understanding they build, love crys out for mutual presence, for intimacy, for time spent together.  In the Holy Eucharist, Jesus himself is present:  mysteriously, silently, sacramentally.  That means the Eucharist is where heaven and earth, eternity and time, grace and nature, touch. 

...But simply being quiet in the presence of the Lord is a form of prayer, too.  And it can be a powerful and spirit-filled kind of prayer.  In prayerful silence, we aren't like the couple talking about what's happened during the day, and how we are concerned about our kith and kin and the world around us...The prayer of quiet is like the couple sitting on the porch side by side in the evening who are sharing the time by being together at that time and place, not needing words at all just then.  That quiet time together, when we share it with our Lord, is a great blessing and time when God can work powerfully on our souls.