Depends largely on the suspected complication. In the acutely unwell surgical patient the following baseline investigations are often helpful:

• Full blood count, urea and electrolytes, C- reactive protein (trend rather than absolute value), serum calcium, liver function tests, clotting (don't forget to repeat if on-going bleeding)
• Arterial blood gases
• ECG (+cardiac enzymes if MI suspected)
• Chest x-ray to identify collapse/ consolidation
• Urine analysis for UTI

These will often identify the most common complications.

Special tests

• CT scanning for identification of intra-abdominal abscesses, air and if luminal contrast is used an anastamotic leak
• Gatrograffin enema- for rectal anastamotic leaks
• Doppler USS of leg veins- for identification of DVT
• CTPA for PE
• Sending peritoneal fluid for U+E (if ureteric injury suspected) or amylase (if pancreatic injury suspected)
• Echocardiogram if pericardial effusion suspected post cardiac surgery and no pleural window made.