A Contractor submits a late CE well pass the 8 week window. How can a PM assess this in a legitimate way and reach a compromise?
Assuming it is one of the compensation events which is subject to the 8 week time bar, the answer is you do not (have to) assess it. You ignore - but probably tell them in some way (under NEC3 because there is no specific contractual response) and ‘reply’ (under clause 61.4 of NEC4) to the Contractor that they are out of time and therefore that the Prices, Completion Date and any Key Dates will not be changed.
That is the strict contractual path. Note though that
(a) it presumes that it is not one of the compensation vents which the Project Manager should have notified - see clause 61.1 - for which there is no time bar; and
(b) that for fairness / relationships etc you may wish to give the Contractor something. However, that shouldn’t be the decision of the Project Manager as it is outside their powers under the contract, but a supplementary agreement between the Employer and Contractor.
When you say submit, it depends on what part of the CE process you are talking about. They should notify the CE within 8 weeks otherwise they are time-barred - assuming it is one of the ones they are obligated to notify (where a PM has instructed a change to the Works Information these are not time-barred).
If it is the quotation process that has been delayed then they should assess it in accordance with 63.1 which would be forecast Defined Cost at the point the event was instructed, or for all other events when the compensation event was notified.