You will need to take an enormous rootball, take as much of the surrounding soil as you can.

Even if it takes 2 people to do it because otherwise you're likely to lose the clematis - they loathe root disturbance and will die if you even tickle a root ( i did that last year and bingo - dead plant).

The rose will transplant a bit easier but still make sure that you have a big rootball again.
The bigger the rootball the easier it is for the plant to settle down.
If you dig INTO the roots the plants will take the rest of the year to settle down.

You don't say why they are to be moved. If it is due to moving house. Dig them up, as Louise says, with as much soil intact around the rootball, if you ar moving location, then put them in a big enough pot to accomodate the ball, keep them well watered and fed, until such time a they can be planted in soil permanently. If it is just to relocate them to a new position, prepare the new site, with plenty of compost, rotted manure etc, water the hole well before planting, replace soil around roots and keep watered through the summer months.