One thing we sometimes do if we're competing large contracts is to run a prequalification round. We decide up front what characteristics we would expect to see in a competent supplier, and what characteristics we'd want to avoid. (eyec's list is a good starting point)
Everybody who expresses an interest gets a questionnaire seeking evidence of competence in these areas - the evidence we ask for depends on the area, ranging from the "describe your approach to....." )which works right up until the moment they buy in a consultant to answer the question for them) through to "List all the times you've been taken to the employment tribunal in the last 5 years".
We decide beforehand whether there are any responses which would automatically disqualify a bidder, how we'll weight and score different levels of response above that, and where we'll set the pass/fail threshold. The process also involves an assessment of financial stability and capacity to perform the work based on the last couple of years' accounts.
Those who get through this process get invited to submit a formal tender.
It sounds bureaucratic, but for large contracts (particularly those burdened by having to conform to EU Public Procurement regulations) it works surprisingly effectively.
Key tips are
0. Do your bidder qualification BEFORE you've involved the interested parties in all the expense of preparing a full bid. Chuck the dud ones out before they've made too great an investment, and they have less incentive to sue.
1. Set your downselect criteria up-front
2. Only ask a question if you really care about the answer
3. Stick with your criteria - if you bend the rules to let someone in even though they don't quite qualify, the decision will probably come back to haunt you.
4. Once you've established a firm is competent, let them bid and make your selection only on product and price.
A.