"What do you say when you don't know what to say? What might be going on in times of silence? Where do these thoughts take you in scripture?"
I would agree with Paget & McCormack (P&M) that we shouldn't try to fix the situation or offer platitudes (10). I would also affirm the power of presence and silence. However, P&M also state that keeping watch involves "active emotional and spiritual presence" (9). While there will certainly be appropriate and necessary moments of what I would consider passive silence, as ministers I think there are situation-appropriate ways to actively administer a message of hope, encouragement, and/or comfort. In times when we don't know what to say are prime times when our voices (thoughts, advice, words of comfot, etc.) need to yield to the voice of God (specifically scripture). These, of course, need to be contextualized and guided by the voice of the Holy Spirit in love and grace and full of compassion and honesty.
Times of silence are prime opportunities for the Spirit to speak to everyone. We need to allow Him the room to speak for Himself (on his own accord), but I think God speaks powerfully through his word. When I don't know what to say, I ask myself "what does scripture say?" One way to avoid the "platitude-ness" is to approach people with the Word with honesty and transparency. For one example, Hebrews 11 shows us a historical timeline of the pain of loss and disappointment for people (and for the blessed people of God no less) but rather the power of faithfulness - the faithfulness of God and the blessings of being faithful to God through our pain.
We must show that we hurt with people. We must respect and value the ministry of presence (and silence), but I also think that as ministers of God people want, need, and expect us to carry a message from Him to them.